<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">LEI SHI</style></author><author><style face="normal" font="default" size="100%">HUA LIU</style></author><author><style face="normal" font="default" size="100%">YUMEI WEI</style></author><author><style face="normal" font="default" size="100%">MING MA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">COMPLEX NON-UNIQUE DYNAMICS IN A HOST-PARASITOID MODEL INCORPORATING CLUMPING EFFECT</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C</style></keyword><keyword><style  face="normal" font="default" size="100%">65C</style></keyword><keyword><style  face="normal" font="default" size="100%">92B</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">09/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/1/1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper, computer simulation is used to study the influence of&amp;nbsp;clumping effect on the dynamic complexities of a discrete-time host-parasitoid model.&amp;nbsp;We report here parasitoid aggregation may be a strong stabilizing or destabilizing&amp;nbsp;factor. Using computer simulation, many forms of complex dynamic are observed,&amp;nbsp;including Hopf bifurcation reversal, period-halving, attractor crises, chaotic bands&amp;nbsp;with narrow or wide periodic windows, intermittent chaos, and supertransient behavior. Several types of attractors, e.g. point equilibrium vs. chaotic, periodic vs.&lt;br /&gt;
quasiperiodic and quasiperiodic vs. chaotic attractors, may coexist in the same mapping. This non-uniqueness also indicates that the bifurcation diagrams, or the routes&amp;nbsp;to chaos, depend on initial conditions and are therefore non-unique. The basins of&amp;nbsp;attraction, defining the initial conditions leading to a certain attractor, may be frac&amp;nbsp;tal set. The fractal property observed is the pattern of self-similarity. The numerical&amp;nbsp;results indicate that computer simulation is a useful method of investigating complex&amp;nbsp;dynamic systems. We also conclude that non-unique dynamic, associated with the&amp;nbsp;extremely complex structure of the basin boundaries, can have a profound effect on&amp;nbsp;our understanding of the dynamical processes of nature.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">1</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">C.S. RYOO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">DIFFERENTIAL EQUATIONS ASSOCIATED WITH DEGENERATE TANGENT POLYNOMIALS AND COMPUTATION OF THEIR ZEROS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">05A19</style></keyword><keyword><style  face="normal" font="default" size="100%">11B83</style></keyword><keyword><style  face="normal" font="default" size="100%">34A30</style></keyword><keyword><style  face="normal" font="default" size="100%">65L99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2019</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/1/9.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper, we study differential equations arising from the generating functions of degenerate tangent polynomials. We give explicit identities for&amp;nbsp;the degenerate tangent polynomials. Finally, we observe an interesting phenomenon&amp;nbsp;of “scattering” of the zeros of degenerate tangent polynomials of higher order.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">153</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">YOUSEF ALNAFISAH</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE EXACT COUPLING WITH TRIVIAL COUPLING (COMBINED METHOD) IN TWO-DIMENSIONAL SDE WITH NON-INVERTIBLITY MATRIX</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">60Hxx</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2019</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/1/7.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">32</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;&amp;nbsp;In &amp;nbsp;Davie \cite{b2} paper, he assumed that the matrix $\big(b_{ik}(x)\big)$ is invertible for all $x$, but in this paper we will show how we could control the matrix which is non-invertible for some $x$ using the (\textit{Combined method}). We describe a method for non-invertibility case (\textit{Combined method}) and we investigate its convergence order which will give $O(h^{3/4}\sqrt{|\log(h)|})$ under some conditions. Moreover we compare the computational results for the combined method with its theoretical error bound and we have obtained a good agreement between them.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">111</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">HONGMEI BAO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE AND STABILITY OF ANTI PERIODIC SOLUTION FOR FCNNS WITH VARIABLE COEFFICIENTS IN THE LEAKAGE TERMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K13</style></keyword><keyword><style  face="normal" font="default" size="100%">34K20</style></keyword><keyword><style  face="normal" font="default" size="100%">92B20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">02/2019</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/2/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;This paper is concerned with the problem of anti periodic solution&amp;nbsp;for a class of fuzzy cellular neural networks (FCNNs) with variable coefficients in&amp;nbsp;the leakage terms. Using contraction mapping and fixed point theorem and differential inequality, we obtain some sufficient conditions to guarantee the existence and&amp;nbsp;exponential stability of the anti periodic solution for this model. These results complement previously known publications. Moreover a numerical example is given to&amp;nbsp;show effectiveness of results obtained.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">275</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RAZIYE MERT</style></author><author><style face="normal" font="default" size="100%">ALLAN PETERSON</style></author><author><style face="normal" font="default" size="100%">THABET ABDELJAWAD</style></author><author><style face="normal" font="default" size="100%">LYNN ERBE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE AND UNIQUENESS OF SOLUTIONS OF NABLA FRACTIONAL DIFFERENCE EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">asymptotic property</style></keyword><keyword><style  face="normal" font="default" size="100%">contraction mapping theorem</style></keyword><keyword><style  face="normal" font="default" size="100%">existence and uniqueness</style></keyword><keyword><style  face="normal" font="default" size="100%">nabla fractional difference equation</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">02/2019</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/1/11.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper, we reformulate certain nabla fractional difference equations which had been investigated by other researchers. The previous results seem&amp;nbsp;to be incomplete. By using Contraction Mapping Theorem, we establish conditions&amp;nbsp;under which solutions exist and are unique and have certain asymptotic properties.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">183</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">K.K. KENZHEBAEV</style></author><author><style face="normal" font="default" size="100%">A.N. STANZHYTSKYI</style></author><author><style face="normal" font="default" size="100%">A.O. TSUKANOVA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE AND UNIQUENESS RESULTS, THE MARKOVIAN PROPERTY OF SOLUTION FOR A NEUTRAL DELAY STOCHASTIC REACTION-DIFFUSION EQUATION IN ENTIRE SPACE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K40</style></keyword><keyword><style  face="normal" font="default" size="100%">34K50</style></keyword><keyword><style  face="normal" font="default" size="100%">60H15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">10/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/1/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">28</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;We establish results, concerning existence, uniqueness, and continuous dependence on an initial datum of a mild solution for neutral stochastic integro-differential equations with variable time delay of reaction-diffusion type. We also establish the Markovian property of this solution. Herewith our emphasis is on unbounded domain $\{x \in \mathbb{R}^{d}\}$.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">19</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">GEORGE E. CHATZARAKIS</style></author><author><style face="normal" font="default" size="100%">IRENA JADLOVSKA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXPLICIT CRITERIA FOR THE OSCILLATION OF DIFFERENTIAL EQUATIONS WITH SEVERAL ARGUMENTS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K06</style></keyword><keyword><style  face="normal" font="default" size="100%">34K11</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">02/2019</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/2/1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">26</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper we are concerned with the oscillations of differential&amp;nbsp;equations with several non-monotone deviating arguments and nonnegative coefficients.&amp;nbsp;We present new sufficient conditions, involving lim sup and lim inf, for the&amp;nbsp;oscillation of all solutions which essentially improve several known criteria existing&amp;nbsp;in the literature. We illustrate the results and the improvement over other known&amp;nbsp;oscillation criteria by examples, numerically solved in MATLAB.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">217</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SUPAKNAREE SATTASO</style></author><author><style face="normal" font="default" size="100%">KAMSING NONLAOPON</style></author><author><style face="normal" font="default" size="100%">HWAJOON KIM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">FURTHER PROPERTIES OF LAPLACE-TYPE INTEGRAL TRANSFORMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A25</style></keyword><keyword><style  face="normal" font="default" size="100%">34A35</style></keyword><keyword><style  face="normal" font="default" size="100%">44A05</style></keyword><keyword><style  face="normal" font="default" size="100%">44A10</style></keyword><keyword><style  face="normal" font="default" size="100%">44A20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2019</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/1/12.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">22</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper, we study some properties of Laplace-type integral&amp;nbsp;transforms, which have been introduced as a computational tool for solving differential&amp;nbsp;equations, and present some examples to illustrate the effectiveness of its applicability.&amp;nbsp;Moreover, we give an example that cannot be solved by Laplace, Sumudu, and Elzaki&amp;nbsp;transforms, but it can be solved by Laplace-type integral transforms; this means&lt;br /&gt;
that Laplace-type integral transforms are a powerful tool for solving some differential&amp;nbsp;equations with variable coefficients.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">195</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ANDREY ANTONOV</style></author><author><style face="normal" font="default" size="100%">SVETOSLAV NENOV</style></author><author><style face="normal" font="default" size="100%">TSVETELIN TSVETKOV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">IMPULSIVE CONTROLABILITY OF TUMOR GROWTH</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A37</style></keyword><keyword><style  face="normal" font="default" size="100%">49N25</style></keyword><keyword><style  face="normal" font="default" size="100%">97M60</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2019</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/1/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this article we introduce some impulsive models of tumor growth&amp;nbsp;based on classical models as inhibition model, Piantadosi model, and autostimulation&amp;nbsp;model. The basic goal is to describe the medical interventions during the treatment&amp;nbsp;of the cancer process.&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;The used technique is based on the theory of impulsive differential equations.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">93</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. HRISTOVA</style></author><author><style face="normal" font="default" size="100%">K. IVANOVA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">LIPSCHITZ STABILITY OF DELAY DIFFERENTIAL EQUATIONS WITH NON-INSTANTANEOUS IMPULSES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A37</style></keyword><keyword><style  face="normal" font="default" size="100%">34D20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2019</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/1/10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;The Lipschitz stability for nonlinear differential equations with non-instantaneous impulses and variable delays is studied. The impulses start abruptly&amp;nbsp;at some points and their action continue on given finite intervals. The delay is time&amp;nbsp;variable. Some sufficient conditions for uniform Lipschitz stability and uniform global&amp;nbsp;Lipschitz stability are obtained. Examples are given to illustrate the results.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">167</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">NIKOLAY KYURKCHIEV</style></author><author><style face="normal" font="default" size="100%">ANTON ILIEV</style></author><author><style face="normal" font="default" size="100%">ASEN RAHNEV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A NEW CLASS OF ACTIVATION FUNCTIONS BASED ON THE CORRECTING AMENDMENTS OF GOMPERTZ–MAKEHAM TYPE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">41A46</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">02.2019</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/2/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;We will explore the interesting methodological task for constructing&amp;nbsp;new activation functions using ”correcting amendments” of ”Gompertz-Makeham-type” (GMAF). We also define the new family of recurrence generated activation&amp;nbsp;functions based on ”Gompertz–Makeham correction” - (RGGMAF).&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;We prove upper and lower estimates for the Hausdorff approximation of the sign&amp;nbsp;function by means of this new class of parametric activation functions - (RGGMAF).&amp;nbsp;Numerical examples, illustrating our results are given.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">243</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SOBIA RAFEEQ</style></author><author><style face="normal" font="default" size="100%">SABIR HUSSAIN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A NEW GRONWALL-BELLMAN TYPE INTEGRAL INEQUALITY AND ITS APPLICATION TO FRACTIONAL STOCHASTIC DIFFERENTIAL EQUATION</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26D10</style></keyword><keyword><style  face="normal" font="default" size="100%">34A34</style></keyword><keyword><style  face="normal" font="default" size="100%">39B72</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">02/2019</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/2/3.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;A Gronwall-Bellman type fractional integral inequality has been&amp;nbsp;derived which is a generalization of already existing result. We also discussed the&amp;nbsp;certain characteristics of the solution of a stochastic differential equation with the&amp;nbsp;help of derived result.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">259</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ANTON ILIEV</style></author><author><style face="normal" font="default" size="100%">NIKOLAY KYURKCHIEV</style></author><author><style face="normal" font="default" size="100%">ASEN RAHNEV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A NEW IMPROVEMENT OF TEMBHURNE-SATHE MODIFICATION OF EUCLIDEAN ALGORITHM FOR GREATEST COMMON DIVISOR. IV</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">11A05</style></keyword><keyword><style  face="normal" font="default" size="100%">68W01</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2019</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/1/8.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this note we gave new interpretation of Tembhurne-Sathe modification of Euclidean algorithm for calculation of greatest common divisor (GCD). Our&amp;nbsp;results are different optimized ways of approaches presented in [1]–[26], [44]–[68]. Our&amp;nbsp;approach is about 9% and 69% faster than Tembhurne-Sathe algorithm in iterative&amp;nbsp;and recursive implementations respectively. For computer implementation Visual C#&amp;nbsp;2017 programming environment is used.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">143</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">EKKACHAI KUNNAWUTTIPREECHACHAN</style></author><author><style face="normal" font="default" size="100%">CHANON PROMSAKON</style></author><author><style face="normal" font="default" size="100%">THANIN SITTHIWIRATTHAM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NONLOCAL FRACTIONAL SUM BOUNDARY VALUE PROBLEM FOR A COUPLED SYSTEM OF FRACTIONAL SUM-DIFFERENCE EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A05</style></keyword><keyword><style  face="normal" font="default" size="100%">39A12</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2019</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/1/5.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this article, we study the existence and uniqueness result for a&amp;nbsp;coupled system of fractional sum-difference equations with nonlocal fractional sum&amp;nbsp;boundary conditions, by using the Banach’s fixed point theorem. Finally, we present&amp;nbsp;an example to show the result of this paper.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">73</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SVETOSLAV MARKOV</style></author><author><style face="normal" font="default" size="100%">ANTON ILIEV</style></author><author><style face="normal" font="default" size="100%">ASEN RAHNEV3</style></author><author><style face="normal" font="default" size="100%">NIKOLAY KYURKCHIEV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A NOTE ON THE THREE–STAGE GROWTH MODEL</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">41A46</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">11/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/1/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper we study the one–sided Hausdorff approximation of&amp;nbsp;the generalized cut function by sigmoidal modified three–stage growth model. The&amp;nbsp;model has a certain right of existence insofar as the theory of sigmoidal functions&amp;nbsp;is well developed. The estimates of the value of the best Hausdorff approximation&amp;nbsp;obtained in this article can be used in practice as one possible additional criterion&amp;nbsp;in ”saturation” study. We examine the small data for modeling the growth of red&amp;nbsp;abalone Haliotis Rufescens in Northern California. Numerical examples are presented&lt;br /&gt;
using &lt;em&gt;CAS MATHEMATICA&lt;/em&gt;.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">63</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RAVI AGARWAL</style></author><author><style face="normal" font="default" size="100%">SNEZHANA HRISTOVA</style></author><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ULAM TYPE STABILITY RESULTS FOR NON-INSTANTANEOUS IMPULSIVE DIFFERENTIAL EQUATIONS WITH FINITE STATE DEPENDENT DELAY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">differential equations</style></keyword><keyword><style  face="normal" font="default" size="100%">existence</style></keyword><keyword><style  face="normal" font="default" size="100%">non-instantaneous impulses</style></keyword><keyword><style  face="normal" font="default" size="100%">state dependent delay</style></keyword><keyword><style  face="normal" font="default" size="100%">Ulam type stability</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">10/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/1/3.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper a system with state dependent bounded delay and&amp;nbsp;non-instantaneous impulses is considered. An existence result based on the Banach&amp;nbsp;contraction principle is given. Several sufficient conditions for Ulam-type stability are&amp;nbsp;obtained. An example is given to illustrate our results.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">47</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SHILIANG CHEN</style></author><author><style face="normal" font="default" size="100%">WEIDE LI</style></author><author><style face="normal" font="default" size="100%">ZHIHUI MA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ANALYSIS ON A MODIFIED LESLIE-GOWER AND HOLLING-TYPE II PREDATOR-PREY SYSTEM INCORPORATING A PREY REFUGE AND TIME DELAY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">92D25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/2/12.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">26</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;This paper describes a delayed predator-prey model with modified Leslie-Grower scheme, in which the time delays are regarded as bifurcation parameters. The functional response is considered to be of Holling-type II and incorporates a constant proportional prey refuge. The model is considered from the point of view of persistence and stability for this particular functional response. The asymptotic stability of coexist equilibrium is examined by using constructed Lyapunov function. The delayed system is analyzed with focusing on the gestation delay of predator τ . We investigate the occurrence of Hopf bifurcation in the neighborhood of the positive interior equilibrium. Moreover, the direction of the Hopf bifurcation and the stability of bifurcating periodic solution are analyzed. Finally, numerical simulations are carried out to verify the theoretical results of the paper.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">397</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">HONGMEI BAO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON ANTI-PERIODIC SOLUTIONS FOR FUZZY BAM NEURAL NETWORKS WITH CONSTANT DELAYS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K13</style></keyword><keyword><style  face="normal" font="default" size="100%">34K20</style></keyword><keyword><style  face="normal" font="default" size="100%">92B20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/3/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;By applying analysis method on time scales and constructing suitable Lyapunov functional, some sufficient conditions are established for the existence and global exponential stability of anti-periodic solutions for a kind of fuzzy BAM neural networks on time scales. Moreover an example is given to illustrate our results.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">545</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JINGYUN LV</style></author><author><style face="normal" font="default" size="100%">XIAOYUAN YANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">APPROXIMATE CONTROLLABILITY OF HILFER FRACTIONAL NEUTRAL STOCHASTIC DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">34A08</style></keyword><keyword><style  face="normal" font="default" size="100%">34K37</style></keyword><keyword><style  face="normal" font="default" size="100%">34K50</style></keyword><keyword><style  face="normal" font="default" size="100%">93B05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">09/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/4/1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">24</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper, we investigate the approximate controllability of Hilfer fractionalneutral stochastic differential equations. Firstly, the existence and uniqueness of&amp;nbsp;mild solutions for these equations are obtained by means of the Banach&amp;nbsp;contraction mapping principle. Then, combining the techniques of stochastic&amp;nbsp;analysis theory, fractional calculations and operator semigroup theory, a new set&amp;nbsp;of sufficient conditions for approximate controllability of these equations is&amp;nbsp;formulated. At last, an example is presented to illustrate the obtained results.&lt;br /&gt;
&amp;nbsp;&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">691</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ALKA CHADHA</style></author><author><style face="normal" font="default" size="100%">S.N. BORA</style></author><author><style face="normal" font="default" size="100%">R. SAKTHIVEL</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">APPROXIMATE CONTROLLABILITY OF IMPULSIVE STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K30</style></keyword><keyword><style  face="normal" font="default" size="100%">34K37</style></keyword><keyword><style  face="normal" font="default" size="100%">35R11</style></keyword><keyword><style  face="normal" font="default" size="100%">47N20</style></keyword><keyword><style  face="normal" font="default" size="100%">60H15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/1/1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">30</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;This paper studies the approximate controllability of an impulsive&amp;nbsp;neutral stochastic integro-differential equation with nonlocal conditions and infinite&amp;nbsp;delay involving the Caputo fractional derivative of order $q\in(1,2)$&amp;nbsp;in separable Hilbert&amp;nbsp;space. The existence of the mild solution to fractional stochastic system with nonlocal and impulsive conditions is first proved utilizing fixed point theorem, stochastic&amp;nbsp;analysis, fractional calculus and solution operator theory. Then, a new set of sufficient conditions proving approximate controllability of nonlocal semilinear fractional stochastic system involving impulsive effects is derived by assuming the associated linear system is approximately controllable. Illustrating the obtained abstract results,&amp;nbsp;an example is considered at the end of the paper.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">1</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">URVASHI ARORA</style></author><author><style face="normal" font="default" size="100%">N. SUKAVANAM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">APPROXIMATE CONTROLLABILITY OF SEMILINEAR FRACTIONAL STOCHASTIC SYSTEM WITH NONLOCAL CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">93B05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.acadsol.eu/dsa/articles/27/1/3.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;This paper deals with the approximate controllability of semilinear&amp;nbsp;fractional stochastic system of order $\rho&amp;nbsp;∈ (1, 2]$ with nonlocal conditions. By using&amp;nbsp;Sadovskii’s fixed point theorem with fractional calculus and stochastic analysis theory,&amp;nbsp;we derive a new set of sufficient conditions for the approximate controllability of&amp;nbsp;fractional stochastic system with nonlocal conditions under the assumption that the&amp;nbsp;corresponding linear system is approximately controllable. Finally, an application to&amp;nbsp;a fractional stochastic system with nonlocal initial conditions is provided to illustrate&lt;br /&gt;
the feasibility of the obtained results.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">45</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JI-HUN YOON</style></author><author><style face="normal" font="default" size="100%">SOTHEARA VENG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ASYMPTOTIC ANALYSIS FOR PORTFOLIO OPTIMIZATION PROBLEM UNDER AN EXTENDED HESTON’S STOCHASTIC VOLATILITY MODEL</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35Q93</style></keyword><keyword><style  face="normal" font="default" size="100%">90C39</style></keyword><keyword><style  face="normal" font="default" size="100%">90C59</style></keyword><keyword><style  face="normal" font="default" size="100%">91G10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">04/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/2/8.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">22</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper, we study the portfolio optimization problem under an extended Heston stochastic volatility model. By using asymptotic analysis technique, we are able to derive approximations of the optimal value function and the optimal strategy. We give an explicit asymptotic approximation of the optimal strategy for the case of hyperbolic absolute risk aversion utility functions and prove that the leading order term of the optimal strategy recovers the approximation up to the first order of the optimal value function.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">331</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BING XIE</style></author><author><style face="normal" font="default" size="100%">HONGJIE GUO</style></author><author><style face="normal" font="default" size="100%">JING LI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">CONTINUITY OF EIGENVALUES IN WEAK TOPOLOGY FOR REGULAR STURM-LIOUVILLE PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">04/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/2/9.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper is concerned with the eigenvalue problems of SturmLiouville differential expressions with general separated boundary conditions. With the aid of properties of analytic functions, only under the standard integrability conditions, we obtain the continuity of eigenvalues in the weak topology of $L^1 [a, b]$ on all the coefficient functions of the differential expressions.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">353</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SHUFAN WANG</style></author><author><style face="normal" font="default" size="100%">WENTING WANG</style></author><author><style face="normal" font="default" size="100%">HUA LIU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A DELAYED PREDATOR-PREY MODEL WITH HOLLING IV FUNCTIONAL RESPONSE AND PREY REFUGE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K18</style></keyword><keyword><style  face="normal" font="default" size="100%">37C75</style></keyword><keyword><style  face="normal" font="default" size="100%">92B05</style></keyword><keyword><style  face="normal" font="default" size="100%">92D25</style></keyword><keyword><style  face="normal" font="default" size="100%">93D20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">07/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/3/14.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;A delay-induced predator-prey model with Holling IV functional&amp;nbsp;response and effect of prey refuge is proposed. The globally asymptotically stability&amp;nbsp;of the coexist equilibrium and Hopf bifurcation are investigated by the theory of the&amp;nbsp;differentially dynamical system. The results show that there exist stability switches&amp;nbsp;and Hopf bifurcation occurs while the gestation delay cross a threshold value.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">663</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">GEORGE E. CHATZARAKIS</style></author><author><style face="normal" font="default" size="100%">IRENA JADLOVSKA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">DIFFERENCE EQUATIONS WITH SEVERAL NON-MONOTONE DEVIATING ARGUMENTS: ITERATIVE OSCILLATION TESTS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A21</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">03/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/2/5.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">28</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;This paper is a study on the oscillatory behavior of the solutions of a&amp;nbsp;difference equation with several non-monotone deviating arguments and nonnegative&amp;nbsp;coefficients. New sufficient oscillation conditions involving lim sup are established&amp;nbsp;using an iterative method. The conditions obtained by this method achieve a marked&amp;nbsp;improvement on all known conditions, requiring at the same time far fewer iterations&amp;nbsp;to determine whether all solutions of the considered equations oscillate, than the&amp;nbsp;other known conditions. Examples, numerically solved in &lt;em&gt;MATLAB&lt;/em&gt;, are provided to&amp;nbsp;illustrate the results and the improvement achieved.&lt;br /&gt;
&amp;nbsp;&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">271</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ZHENSHU WEN</style></author><author><style face="normal" font="default" size="100%">LIJUAN SHI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">DYNAMICS OF BOUNDED TRAVELING WAVE SOLUTIONS FOR THE MODIFIED NOVIKOV EQUATION</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35C07</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">06/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/3/8.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper, we study the bifurcations and dynamics of bounded traveling wave solutions for the modified Novikov equation by combining the factorization technique and the method of dynamical systems. We show that the corresponding traveling wave system is a singular planar dynamical system with two singular straight lines, and obtain all possible phase portraits of the system. Then we show the existence and dynamics of several types of bounded traveling wave solutions including solitary wave solutions, periodic wave solutions, compacton solutions, kink-like and antikink-like solutions. The dynamics of these new bound traveling wave solutions will significantly facilitate nonlinear wave theories.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">581</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JIHOON LEE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">DYNAMICS OF GLOBAL ATTRACTOR FOR A SEMILINEAR DEGENERATE PARABOLIC EQUATION INVOLVING GRUSHIN OPERATORS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35B05</style></keyword><keyword><style  face="normal" font="default" size="100%">35J70</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/3/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper we study the dynamics of global attractor of a semilinear parabolic equation involving Grushin operators. First we show that the global attractor is bounded in ${ L^∞(Ω) }$ and ${ D(A) }$. Then we investigate the existence of a Lyapunov function, the injectivity on the global attractor and the squeezing property. Finally, we obtain estimates on upper bound and lower bound of the fractal dimension of the global attractor.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">457</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ARJUMAND SEEMAB</style></author><author><style face="normal" font="default" size="100%">MUJEEB UR REHMAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE AND STABILITY ANALYSIS BY FIXED POINT THEOREMS FOR A CLASS OF NON-LINEAR CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/3/1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;The main purpose of this work is to establish existence result and stability criteria for a class of fractional order differential equations using fixed point theorems. Existence results are based on Schauder’s fixed point theorem, Banach contraction principle and, emphasis is put on the application of the Krasnoselskii’s fixed point theorem to establish stability criteria of a specific class of fractional order differential equations. An example is given to show the usefulness of the stability result.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">445</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">PRADEEP G. CHHETRI</style></author><author><style face="normal" font="default" size="100%">AGHALAYA S. VATSALA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF THE SOLUTION IN THE LARGE FOR CAPUTO FRACTIONAL REACTION DIFFUSION EQUATION BY PICARD’S METHOD</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A08</style></keyword><keyword><style  face="normal" font="default" size="100%">34R11</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">11/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/4/10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this work, we have developed Picard's iterative method to prove the existence and uniqueness of the solution of the nonlinear Caputo fractional reaction diffusion equation in one dimensional space. The order of the fractional time derivative q is such that $0.5\leq q\leq 1$. The existence result has been proved by a priori assuming the solution is bounded. Thus, we refer to this method as existence of solution in the large. The method can be &amp;nbsp;extended to the Caputo fractional reaction diffusion system also.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">837</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MOHAMMAD REZA HEIDARI TAVANI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE RESULTS FOR FOURTH-ORDER ELASTIC BEAM EQUATIONS ON THE REAL LINE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">34B40</style></keyword><keyword><style  face="normal" font="default" size="100%">47H14</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.acadsol.eu/dsa/articles/27/1/8.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The existence and multiplicity of solutions for a perturbed fourthorder&amp;nbsp;problem on the real line with a perturbed nonlinear term depending on one real&amp;nbsp;parameter is investigated. Our approach is based on variational&amp;nbsp; methods and critical&amp;nbsp;point theory which are obtained in [3].&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">149</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SHAFIQUL ISLAM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A FAMILY OF RANDOM MAPS WHICH POSSES INFINITE ABSOLUTELY CONTINUOUS INVARIANT MEASURES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">37A05</style></keyword><keyword><style  face="normal" font="default" size="100%">37H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">09/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/4/3.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;We consider a family of random maps where each of the component&amp;nbsp;maps is from a family of piecewise, linear and Markov maps on a class of infinite&amp;nbsp;partitions of the state space. We investigate the existence of infinite absolutely continuous&amp;nbsp;invariant measures of the random maps. In a more general setting, our study&amp;nbsp;establishes a positive answer to the question in discrete time dynamical system: can&amp;nbsp;two chaotic systems give rise to order, namely can they be combined into another&amp;nbsp;dynamical system which does not behave chaotically? This question is analogous to&amp;nbsp;Parrondo’s paradox [5] which states that two losing gambling games when combined&amp;nbsp;one after the other (either deterministically or randomly) can result in a winning&amp;nbsp;game: that is, a losing game followed by a losing game = a winning game.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">729</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">GENERAL LEFSCHETZ FIXED POINT THEORY FOR MULTIVALUED MAPS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword><keyword><style  face="normal" font="default" size="100%">54C60</style></keyword><keyword><style  face="normal" font="default" size="100%">54H25</style></keyword><keyword><style  face="normal" font="default" size="100%">55M20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">10/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/4/8.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;Some generalizations of the Lefschetz fixed point theorem are presented&amp;nbsp;for admissible maps on Hausdorff topological spaces.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">803</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MEIHUA DONG</style></author><author><style face="normal" font="default" size="100%">SANGJIN KIM</style></author><author><style face="normal" font="default" size="100%">JIANDONG YIN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">GROUP ACTIONS WITH TOPOLOGICALLY STABLE MEASURES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">37C85</style></keyword><keyword><style  face="normal" font="default" size="100%">54H20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.acadsol.eu/dsa/articles/27/1/10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;We prove that if an action $T$ of a finitely generated group $G$ on a compact metric space $X$ is measure expansive and has the measure shadowing property then it is measure topologically stable. This represents a measurable version of the main result in [4]. Moreover we prove that if $G$ is a finitely generated virtually nilpotent group and there exists $g \in G$ such that $T_g$ is expansive and has the invariant measure shadowing property then $T$ is invariant measure topologically stable. Finally we show that minimal actions approximated by periodic ones have no topologically stable measures.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">185</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">OCTAVIA-MARIA BOLOJAN</style></author><author><style face="normal" font="default" size="100%">RADU PRECUP</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">HYBRID DELAY EVOLUTION SYSTEMS WITH NONLINEAR CONSTRAINTS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K30</style></keyword><keyword><style  face="normal" font="default" size="100%">35K90</style></keyword><keyword><style  face="normal" font="default" size="100%">47J35</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">09/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/4/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;Motivated by the importance of reaction-diffusion systems in modeling&amp;nbsp;real processes with memory, we are interested in the existence of mild solutions&amp;nbsp;for systems of abstract delay evolution equations subjected to general nonlinear constraints.&amp;nbsp;Wishing to allow the system nonlinearities to behave independently as much&amp;nbsp;as possible, we use a vector approach based on matrices, vector-valued norms and a&amp;nbsp;vector version of Krasnoselskii’s fixed point theorem for a sum of two operators. The&amp;nbsp;hybrid character of the systems comes from the different nature of the metrical and&amp;nbsp;topological conditions imposed to the component equations. Also, the assumptions&amp;nbsp;are put in connection with the support of the nonlinear constraints. Two examples&amp;nbsp;are given to illustrate the theory.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">773</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">GUANGYING LV</style></author><author><style face="normal" font="default" size="100%">JINQIAO DUAN</style></author><author><style face="normal" font="default" size="100%">LIANG WANG</style></author><author><style face="normal" font="default" size="100%">JIANG-LUN WU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">IMPACTS OF NOISE ON ORDINARY DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35K20</style></keyword><keyword><style  face="normal" font="default" size="100%">60H15</style></keyword><keyword><style  face="normal" font="default" size="100%">60H40</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">03/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/2/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we consider the impacts of noise on ordinary differential&amp;nbsp;equations. We first prove that the weak noise can change the value of equilibrium&amp;nbsp;and the strong noise can destroy the stability of equilibrium. Then we consider the&amp;nbsp;competition between the nonlinear term and noise term, which shows that noise can&amp;nbsp;induce singularities (finite time blow up of solutions) and that the nonlinear term&amp;nbsp;can prevent the singularities. Besides that, some simulations are given in order to&amp;nbsp;illustrate our results.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">225</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ANDREY  ANDREEV</style></author><author><style face="normal" font="default" size="100%">MILENA  RACHEVA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">INTERPOLATED FINITE ELEMENT METHOD FOR SOME FOURTH-ORDER ELLIPTIC PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">65D10</style></keyword><keyword><style  face="normal" font="default" size="100%">65N12</style></keyword><keyword><style  face="normal" font="default" size="100%">65N15</style></keyword><keyword><style  face="normal" font="default" size="100%">65N25</style></keyword><keyword><style  face="normal" font="default" size="100%">65N30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/2/13.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">22</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;We introduce nonstandard interpolated finite elements providing better accuracy for a fourth-order elliptic boundary value problems, as well as to the biharmonic eigenvalue problems. The term ”ultraconvergence” indicates that the convergence rate is at least two orders higher than the optimal global rate. This method is a variant of a postprocessing procedure when the known finite element solution is used. Moreover, a posteriori error estimates of global ultraconvergent type are derived. The presented approach is applicable for the general rectangular finite element meshes. Some numerical results illustrate the efficiency of the proposed algorithm.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">423</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MIAOMIAO GAO</style></author><author><style face="normal" font="default" size="100%">FENG HU</style></author><author><style face="normal" font="default" size="100%">ZHAOJUN ZONG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">LAW OF LARGE NUMBERS AND CENTRAL LIMIT THEOREM FOR INDEPENDENT AND NON-IDENTICAL DISTRIBUTED RANDOM VARIABLES UNDER SUBLINEAR EXPECTATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">60G48</style></keyword><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">03/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/2/3.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper, we study some limit theorems for random variables under sublinear expectations. First, a law of large numbers is proved for independent and non-identical distributed random variables with only finite first order moments. Second, a central limit theorem is proved for independent and non-identical distributed random variables with only finite second order moments. These results include and extend some existing results.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">237</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">G. YIN</style></author><author><style face="normal" font="default" size="100%">G. ZHAO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A LIMIT RESULT ASSOCIATED WITH CERTAIN RANDOM TWO-POINT BOUNDARY VALUE PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B99</style></keyword><keyword><style  face="normal" font="default" size="100%">60F05</style></keyword><keyword><style  face="normal" font="default" size="100%">60J60</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/1/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;A nonlinear differential equation with wide-band random noise and&amp;nbsp;random boundary conditions is considered in this work. Our main effort is on obtaining&amp;nbsp;a diffusion limit using weak convergence methods. The limit can be used as&amp;nbsp;approximation to the original problem leading to reduction of computational complexity.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">31</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">K.C. NGUYEN</style></author><author><style face="normal" font="default" size="100%">T.V. NHUNG</style></author><author><style face="normal" font="default" size="100%">T.T. ANH HOA</style></author><author><style face="normal" font="default" size="100%">N.C. LIEM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">LYAPUNOV EXPONENTS FOR DYNAMIC EQUATIONS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26E70</style></keyword><keyword><style  face="normal" font="default" size="100%">34N05</style></keyword><keyword><style  face="normal" font="default" size="100%">37D25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">04/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/2/10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we deal with a concept of Lyapunov exponents for functions defined on time scales and study some its basic properties. We also establish the relationship between Lyapunov exponents and the stability of linear dynamic equations. This work can be considered as a unification and generalization of investigations of Lyapunov exponents on continuous and discrete times.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">367</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MANSEOB LEE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MEASURE EXPANSIVENESS FOR C1 GENERIC DIFFEOMORPHISMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34D10</style></keyword><keyword><style  face="normal" font="default" size="100%">37D30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">07/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/3/11.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let M be a closed smooth Reimannian manifold, and let $f : M \to&amp;nbsp;M$ be a diffeomorphism. In the paper, we show that $C^1$&amp;nbsp;generically, a diffeomorphism $f$ is measure expansive then it is Axiom A without cycles.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">629</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SVETOSLAV MARKOV</style></author><author><style face="normal" font="default" size="100%">NIKOLAY KYURKCHIEV</style></author><author><style face="normal" font="default" size="100%">ANTON ILIEV</style></author><author><style face="normal" font="default" size="100%">ASEN RAHNEV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A NOTE ON THE LOG–LOGISTIC AND TRANSMUTED LOG–LOGISTIC MODELS. SOME APPLICATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">41A46</style></keyword><keyword><style  face="normal" font="default" size="100%">68N30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">07/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/3/9.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;The Hausdorff approximation of the shifted Heaviside function by&amp;nbsp;Log-logistic and quadratic transmuted Log-logistic sigmoid functions is investigated&amp;nbsp;and an expression for the error of the best approximation is obtained. The results of&amp;nbsp;numerical examples performed in the programming environmentMathematica confirm&amp;nbsp;our theoretical conclusions. Some applications in the field of biochemical processes&amp;nbsp;and debugging theory are also explored.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">593</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RICARDO AGUILAR-LOPEZ</style></author><author><style face="normal" font="default" size="100%">JUAN  MATA-MACHUCA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE OBSERVABILITY AND STATE ESTIMATION IN A CLASS OF GENE-EXPRESSION SYSTEM</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A34</style></keyword><keyword><style  face="normal" font="default" size="100%">92B05</style></keyword><keyword><style  face="normal" font="default" size="100%">93B07</style></keyword><keyword><style  face="normal" font="default" size="100%">93E10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/3/5.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;The failure of available physical sensors for the online measurement of protein concentration in cells is a key problem to understanding the transition in bio-systems. In this paper, a new state observer has been designed to estimate three protein concentrations by using a gene-expression mathematical model. Interestingly, its only input is the concentration of one messenger RNA (mRNA). Similarly by differential-algebraic observability analysis is showed that the gene-expression model is indeed observable. The observer convergence was demonstrated by analysing the estimation error dynamics. In silico experiments confirm the satisfactory performance of this new observer.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">531</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">G.E. CHATZARAKIS</style></author><author><style face="normal" font="default" size="100%">M. DEEPA</style></author><author><style face="normal" font="default" size="100%">N. NAGAJOTHI</style></author><author><style face="normal" font="default" size="100%">V. SADHASIVAM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE OSCILLATION OF THREE DIMENSIONAL alpha-FRACTIONAL DIFFERENTIAL SYSTEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A08</style></keyword><keyword><style  face="normal" font="default" size="100%">34A34</style></keyword><keyword><style  face="normal" font="default" size="100%">34K11</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">11/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/4/12.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">22</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this article, we consider the three dimensional $\alpha$-fractional nonlinear differential system of the form $$ D^{\alpha}\left(x(t)\right)=a(t)f\left(y(t)\right), $$ $$ D^{\alpha}\left(y(t)\right)=-b(t)g\left(z(t)\right), $$ $$ D^{\alpha}\left(z(t)\right)=c(t)h\left(x(t)\right),\quad t \geq t_0, $$ where $0 &amp;lt; \alpha \leq 1$, $D^{\alpha}$ denotes the Katugampola fractional derivative of order $\alpha$. We establish some new sufficient conditions for the oscillation of the solutions of the differential system, using the generalized Riccati transformation and inequality technique. Examples illustrating the results are also given.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">873</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">GRACE, SAID R</style></author><author><style face="normal" font="default" size="100%">JADLOVSKA, IRENA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OSCILLATORY BEHAVIOR OF ODD-ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH A NONPOSITIVE NEUTRAL TERM</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">34K11</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/1/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><isbn><style face="normal" font="default" size="100%">1056-2176</style></isbn><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, sufficient conditions are established for oscillation of all&amp;nbsp;solutions of the odd-order nonlinear differential equations with a nonpositive neutral&amp;nbsp;term. When the neutral term is present, all the results are new even for $n = 3$. An&amp;nbsp;example is given to illustrate the main results.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">125</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">PEKKA KOSUNEN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">PERIODIC ORBITS OF QUADRATIC POLYNOMIALS OF PERIODS SIX AND SEVEN</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">30D05</style></keyword><keyword><style  face="normal" font="default" size="100%">37F10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/1/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">44</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;The dynamics of quadratic polynomials is commonly studied by using&amp;nbsp;the family of maps $f_c (x) = x^2&amp;nbsp;+ c$, where $c\in C$. In this paper we form equations of&amp;nbsp;periodic orbits of periods six and seven on a new $(u, v)$-plane and consider also the&amp;nbsp;corresponding equations on the $(x, y)$-plane. The new $(u, v)$-model produces equations&amp;nbsp;for the periods six and seven with significantly lower degree than the ones obtained&amp;nbsp;by the previous models which enables us to find their solutions.&lt;br /&gt;
&amp;nbsp;&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">63</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">YANG WU</style></author><author><style face="normal" font="default" size="100%">JIAN-PING SUN</style></author><author><style face="normal" font="default" size="100%">YA-HONG ZHAO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">POSITIVE SOLUTIONS OF A FOURTH-ORDER PERIODIC BOUNDARY VALUE PROBLEM WITH PARAMETER</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">07/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/3/12.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we study the following periodic boundary value problem of fourth-order ordinary differential equation&lt;br /&gt;
&amp;nbsp; \begin{equation*}&lt;br /&gt;
&amp;nbsp; \left\{&lt;br /&gt;
&amp;nbsp; &amp;nbsp;\begin{aligned}&lt;br /&gt;
&amp;nbsp; &amp;nbsp;&amp;amp;u^{(4)}(t)+\alpha u^{\prime\prime}(t)-\rho^{4}u(t)+\lambda f(t,u(t))=0,~t\in{[0,2\pi]},\\&lt;br /&gt;
&amp;nbsp; &amp;nbsp;&amp;amp;u^{(i)}(0)=u^{(i)}(2\pi),~i=0,1,2,3,\\&lt;br /&gt;
&amp;nbsp; &amp;nbsp;\end{aligned}&lt;br /&gt;
&amp;nbsp; &amp;nbsp;\right.&lt;br /&gt;
&amp;nbsp; \end{equation*}&lt;br /&gt;
where $\alpha$ and $\rho$ are constants satisfying $\rho\neq0$ and $4\alpha+16\rho^{4}&amp;lt;1$, and $\lambda&amp;gt;0$ is a parameter. By imposing some conditions on the nonlinear term $f$, we obtain the existence and multiplicity of positive solutions to the above problem for suitable $\lambda$. The main tool used is Guo-Krasnoselskii fixed point theorem.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">33</style></issue><section><style face="normal" font="default" size="100%">637</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MIAO HAN</style></author><author><style face="normal" font="default" size="100%">XUEFENG SONG</style></author><author><style face="normal" font="default" size="100%">WEI WANG</style></author><author><style face="normal" font="default" size="100%">HUAWEI NIU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">PRICING EQUITY-LINKED FOREIGN EXCHANGE OPTION UNDER A REGIME-SWITCHING MULTI-SCALE JUMP-DIFFUSION MODEL</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">65C30</style></keyword><keyword><style  face="normal" font="default" size="100%">91B24</style></keyword><keyword><style  face="normal" font="default" size="100%">91B70</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/3/3.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;This paper studies the valuation of equity-linked foreign exchange call option under a regime-switching multi-scale jump diffusion model. The foreign equity price is driven by a regime-switching multi-scale jump-diffusion process and the foreign exchange rate is assumed to follow a regime-switching mean-reversion multiscale jump-diffusion process. In addition, the correlations of the two processes are not only manifested in the diffusion parts but also in the jump components. The measure change and Fourier transform technique are adopted to calculate the price of equitylinked foreign exchange call option. Numerical examples and comparative analysis are also provided by fast Fourier transform algorithm to illustrate our results.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">475</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RENHAI WANG</style></author><author><style face="normal" font="default" size="100%">YANGRONG LI</style></author><author><style face="normal" font="default" size="100%">FUZHI LI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">PROBABILISTIC ROBUSTNESS FOR DISPERSIVE-DISSIPATIVE WAVE EQUATIONS DRIVEN BY SMALL LAPLACE-MULTIPLIER NOISE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35B40</style></keyword><keyword><style  face="normal" font="default" size="100%">35B41</style></keyword><keyword><style  face="normal" font="default" size="100%">37L30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.acadsol.eu/dsa/articles/27/1/9.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;This paper is devoted to limit-dynamics for dispersive-dissipative&amp;nbsp;wave equations on an unbounded domain. An interesting feature is that the stochastic&amp;nbsp;term is multiplied by an unbounded Laplace operator. A random attractor in&amp;nbsp;the Sobolev space is obtained when the density of noise is small and the growth rate&amp;nbsp;of nonlinearity is subcritical. The random attractor is upper semicontinuous to the&lt;br /&gt;
global attractor when the density of noise tends to zero. Both methods of spectrum&amp;nbsp;and tail-estimate are combined to prove the collective limit-set compactness. Furthermore,&amp;nbsp;a probabilistic method is used to show that the robustness of attractors is&amp;nbsp;basically uniform in probability.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">165</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">CHAO TANG</style></author><author><style face="normal" font="default" size="100%">YONG-KUI CHANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">S2γ  -WPAA FUNCTIONS AND APPLICATIONS TO STOCHASTIC NEUTRAL FUNCTIONAL EQUATIONS WITH INFINITE DELAY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C27</style></keyword><keyword><style  face="normal" font="default" size="100%">34D20</style></keyword><keyword><style  face="normal" font="default" size="100%">34F05</style></keyword><keyword><style  face="normal" font="default" size="100%">60H30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/3/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">36</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper, we introduce the concept of ${ S^2_{\gamma}&amp;nbsp;}$ -weighted pseudo almost automorphy. And then, we investigate some basic properties such as completeness of spaces, ergodic and composition theorems of such stochastic processes. Finally, by virtue of theories of evolution systems, fading phase spaces for infinite delay and the stochastic analysis techniques, we apply the results obtained to consider the existence and uniqueness results of weighted pseudo almost automorphic solutions in distribution to a class of nonautonomous stochastic neutral functional equations with infinite delay under ${ S^2_{\gamma}&amp;nbsp;}$ -weighted pseudo almost automorphic coefficients in real separable Hilbert spaces.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">495</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BISHWAL, JAYA P.N.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SEQUENTIAL MAXIMUM LIKELIHOOD ESTIMATION IN NONLINEAR NONMARKOV DIFFUSION TYPE PROCESSES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">37H10</style></keyword><keyword><style  face="normal" font="default" size="100%">60G40</style></keyword><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword><keyword><style  face="normal" font="default" size="100%">62F12</style></keyword><keyword><style  face="normal" font="default" size="100%">62L12</style></keyword><keyword><style  face="normal" font="default" size="100%">62M09</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/1/5.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;We obtain the strong consistency, uniform asymptotic normality and&amp;nbsp;local asymptotic minimaxity (in the Hajek-LeCam sense) of the two stage sequential&amp;nbsp;maximum likelihood estimator of a parameter appearing nonlinearly in the drift&amp;nbsp;coefficient of a stochastic differential equation when the corresponding non-Markov&amp;nbsp;diffusion type process is observed until the observed Fisher information of the process&amp;nbsp;exceeds a predetermined level of precision and the level becomes large. Main results&amp;nbsp;are illustrated by the exponential memory non-Markovian Ornstein-Uhlenbeck&lt;br /&gt;
process.&amp;nbsp;&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">107</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">L. HATVANI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SMITH-TYPE STABILITY THEOREMS FOR THE DAMPED LINEAR OSCILLATOR</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34D20</style></keyword><keyword><style  face="normal" font="default" size="100%">70J25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">03/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/2/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;Sufficient conditions are given guaranteeing that every solution of the equation&lt;/p&gt;

&lt;p class=&quot;rtecenter&quot;&gt;\[x''+h(t)x'+\omega^2x=0 \qquad (h(t)\ge 0,\ x\in {\mathbb{R}})\]&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;and its derivative tend to zero as $t\to\infty$. The results are applicable in the general case $0\le 0\le h(t)&amp;lt;\infty$, i.e., conditions $h(t)\ge$const.$&amp;gt;0$ and $h(t)\le$const.$&amp;lt;\infty$ are not required in general. In the first main theorem the damping is controlled on the whole half-line $[0,\infty)$. The second main theorem is devoted to the problem of the intermittent damping, when &amp;nbsp;conditions are supposed only on the union of non-overlapping intervals.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">299</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">HWAJOON KIM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE SOLUTION OF THE HEAT EQUATION WITHOUT BOUNDARY CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35A22</style></keyword><keyword><style  face="normal" font="default" size="100%">44A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">07/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/3/10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;We would like to propose the solution of the heat equation without&amp;nbsp;boundary conditions. The methodology used is Laplace transform approach, and the&amp;nbsp;transform can be changed another ones. This attempt is more advanced than the&amp;nbsp;existing method and has a meaning in that it is approached in a general way without&amp;nbsp;restricting the boundary conditions. The solution of heat equation is presented by&amp;nbsp;using the property of integrability of transform.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">653</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RATINAN BOONKLURB</style></author><author><style face="normal" font="default" size="100%">KEERATI KAEWRAK</style></author><author><style face="normal" font="default" size="100%">TAWIKAN TREEYAPRASERT</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOLUTION PROFILES BEYOND QUENCHING FOR SINGULAR SEMILINEAR PARABOLIC PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35K35</style></keyword><keyword><style  face="normal" font="default" size="100%">35K57</style></keyword><keyword><style  face="normal" font="default" size="100%">35K61</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">08/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/3/15.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;Let $T\leq\infty,~a&amp;gt;0,$ $0&amp;lt;r&amp;lt;1,~D=(0,a),~\Omega=D\times(0,T]$ and $\chi(S)$ be&amp;nbsp;the characteristic function of the set $S$. This article studies the&amp;nbsp;steady-state solution after quenching has occured of the semilinear parabolic&amp;nbsp;equation with singularity&lt;br /&gt;
\begin{align*}&lt;br /&gt;
&amp;amp; &amp;nbsp;u_{t}-u_{xx}-\frac{r}{x}u_{x}=f(u)\chi(\{u&amp;lt;c\})~\text{in}~\Omega,\\&lt;br /&gt;
&amp;amp; &amp;nbsp;u(x,0)=0~\text{on}~\bar{D},\\&lt;br /&gt;
&amp;amp; &amp;nbsp;u(0,t)=0=u(a,t)~\text{for}~0&amp;lt;t&amp;lt;T.&lt;br /&gt;
\end{align*}&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;It is shown that as $t$ tends to $\infty$, all weak solutions $u\left(x,t\right) &amp;nbsp;$ tend to a unique steady-state solution $U(x)\text{ for }\ 0&amp;lt;{{b}_{s}^{\ast}}\leq x\leq{{B}_{s}^{\ast}}&amp;lt;a$. The numerical methods are&amp;nbsp;developed for computing ${{b}_{s}^{\ast}}$ and ${{B}_{s}^{\ast}}$.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">673</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ATANASKA GEORGIEVA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOLVING TWO-DIMENSIONAL NONLINEAR VOLTERRA-FREDHOLM FUZZY INTEGRAL EQUATIONS BY USING ADOMIAN DECOMPOSITION METHOD</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">45B05</style></keyword><keyword><style  face="normal" font="default" size="100%">45G10</style></keyword><keyword><style  face="normal" font="default" size="100%">65R20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">11/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/4/9.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper, we propose Adomian decomposition method (ADM)&amp;nbsp;to approximate the solution of two-dimensional nonlinear Volterra-Fredholm fuzzy&amp;nbsp;integral equation (2D-NVFFIE). We convert this integral equation to a nonlinear&amp;nbsp;system of Volterra-Fredholm integral equations in crisp case. The aim of this paper&amp;nbsp;is to find an approximate solution of this system using ADM. Hence, we obtain an&amp;nbsp;approximation for the fuzzy solution of the nonlinear Volterra-Fredholm fuzzy integral&amp;nbsp;equation. A numerical example is given to demonstrate the validity and applicability&amp;nbsp;of the proposed technique.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">819</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">AURELIAN CERNEA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOME REMARKS ON THE SOLUTIONS OF A SECOND-ORDER EVOLUTION INCLUSION</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A60</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">04/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/2/7.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;We prove the Lipschitz dependence on the initial data of the solution&amp;nbsp;set of a Cauchy problem associated to a second-order evolution inclusion by using the&amp;nbsp;contraction principle in the space of selections of the multifunction instead of the space&amp;nbsp;of solutions. A Filippov type existence theorem for this problem is also provided.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">319</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SNEZHANA HRISTOVA</style></author><author><style face="normal" font="default" size="100%">PETER KOPANOV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STABILITY OF NEURAL NETWORKS WITH RANDOM IMPULSES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A37</style></keyword><keyword><style  face="normal" font="default" size="100%">34D20</style></keyword><keyword><style  face="normal" font="default" size="100%">34F99</style></keyword><keyword><style  face="normal" font="default" size="100%">92B20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">10/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/4/7.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;One of the main properties of solutions of neural networks is stability&amp;nbsp;and often the direct Lyapunov method is used to study stability properties. We consider the Hopfield’s graded response neural network in the case when the neurons are&amp;nbsp;subject to a certain impulsive state displacement at random exponentially distributed&amp;nbsp;moments. It changes significantly the behavior of the solutions because they are not&amp;nbsp;deterministic ones but they are stochastic processes. We examine the stability of the&amp;nbsp;equilibrium of the model. Some sufficient conditions for p-moment stability of equilibrium of neural networks with time varying self-regulating parameters of all units&amp;nbsp;and time varying functions of the connection between two neurons in the network are&amp;nbsp;obtained. These sufficient conditions are explicitly expressed in terms of the parameters of the system and hence they are easily verifiable. We illustrate our theory on&amp;nbsp;a particular nonlinear neural network.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">791</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">XIANG LIU</style></author><author><style face="normal" font="default" size="100%">BAOGUO JIA</style></author><author><style face="normal" font="default" size="100%">LYNN ERBE</style></author><author><style face="normal" font="default" size="100%">ALLAN PETERSON</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STABILITY RESULTS FOR NONLINEAR FRACTIONAL ORDER h-DIFFERENCE SYSTEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A11</style></keyword><keyword><style  face="normal" font="default" size="100%">39A70</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">07/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/3/10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;This paper is concerned with the stability of the fractional order&amp;nbsp;h-difference systems. The definition of Mittag-Leffler stability is introduced, and the&amp;nbsp;sufficient conditions are presented by extending the Lyapunov direct method to such&amp;nbsp;systems. Moreover, we weaken the restriction on Lyapunov function, the stability of&amp;nbsp;the fractional order h-difference systems is established. Two numerical examples are&amp;nbsp;given to illustrate our main results.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">609</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">K. ANITHA</style></author><author><style face="normal" font="default" size="100%">M.N. SRINIVAS</style></author><author><style face="normal" font="default" size="100%">V. MADHUSUDANAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STOCHASTIC AND DELAY ANALYSIS OF TWO PREYS AND ONE PREDATOR ECOLOGICAL SYSTEM WITH COMPETITION AMONG PREYS AND SELF INTERACTION</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">37C23</style></keyword><keyword><style  face="normal" font="default" size="100%">37G15</style></keyword><keyword><style  face="normal" font="default" size="100%">65L99</style></keyword><keyword><style  face="normal" font="default" size="100%">70K50</style></keyword><keyword><style  face="normal" font="default" size="100%">92B05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">02/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/2/1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">24</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this research article, a two prey-one predator system with intra&amp;nbsp;specific competition and self-interaction is investigated and its dynamics are mathematically analyzed. The positivity of the solution and boundedness of the system&amp;nbsp;is studied. The occurrence of possible equilibrium points and stability of the system&amp;nbsp;at those points is examined. The necessary and sufficient condition for the existence of positive interior equilibrium point $E_ 6 (x^∗ , y^∗ , z^∗ )$ is obtained. Also the point $E_6 (x^∗ , y^∗ , z^∗ )$ is investigated for the local and global stability of the system. Stability&amp;nbsp;of the delayed model is investigated and it is observed that stability of the system is&amp;nbsp;dependent on time delay. Time delay drives the system from stable to unstable state.&amp;nbsp;The system and its value is described by environmental stochasticity in the form of&amp;nbsp;Gaussian white noise. Numerical simulation is&amp;nbsp; performed to justify the analytical&amp;nbsp;findings.&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;&amp;nbsp;&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;&lt;strong&gt;Editorial remark [2018-03-12]:&lt;/strong&gt; The article has been replaced according authors request. The old version of article is available &lt;a href=&quot;https://acadsol.eu/dsa/articles/27/2/1-1.pdf&quot;&gt;here&lt;/a&gt;.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">201</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">PENGYAN ZHANG</style></author><author><style face="normal" font="default" size="100%">WEIGUO YANG</style></author><author><style face="normal" font="default" size="100%">BEI WANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE STRONG LAW OF LARGE NUMBERS FOR MULTIVARIATE FUNCTIONS OF CONTINUOUS-STATE NONHOMOGENEOUS MARKOV CHAINS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">60F15</style></keyword><keyword><style  face="normal" font="default" size="100%">60J05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">03/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/2/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we are going to study the strong law of large numbers for multivariate functions of continuous-state nonhomogeneous Markov chains. Firstly, we give a primary proof of equivalence of the ergodicities for continuous-state homogeneous Markov chains. Then, we establish some lemmas which are the basis of the main result. Finally, we study the strong law of large numbers for functions of N + 1 variables of continuous-state nonhomogeneous Markov chains.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">257</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">T.E. GOVINDAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">TROTTER-KATO APPROXIMATIONS OF McKEAN-VLASOV TYPE STOCHASTIC EVOLUTION EQUATIONS IN HILBERT SPACES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">60H15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/3/7.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;This paper is concerned with a semilinear McKean-Vlasov type Itˆo stochastic evolution equation in a Hilbert space. The goal here is to consider the existence and uniqueness of mild solutions, Trotter-Kato approximations of mild solutions of such equations and also to deduce the weak convergence of the corresponding induced probability measures. As an application, a classical limit theorem on the dependence of such equations on a parameter is obtained. An example on a stochastic heat equation is included at the end.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">565</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">YAN LUO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">UPPER AND LOWER SOLUTIONS METHOD FOR IMPULSIVE DIFFERENTIAL INCLUSIONS WITH NONLINEAR BOUNDARY CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A37</style></keyword><keyword><style  face="normal" font="default" size="100%">34A60</style></keyword><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/2/11.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper discusses the antiperiodic and nonlinear boundary problem for first-order impulsive differential inclusions. We establish the existence results by using Martelli’s fixed point theorem with upper and lower solutions method.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">387</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">LINA MA</style></author><author><style face="normal" font="default" size="100%">D. KANNAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">VALUATION OF REVERSE MORTGAGE WITH DEPENDENT JOINT LIVES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">joint annuity</style></keyword><keyword><style  face="normal" font="default" size="100%">jump-diffusion</style></keyword><keyword><style  face="normal" font="default" size="100%">lifetime model</style></keyword><keyword><style  face="normal" font="default" size="100%">reverse mortgage</style></keyword><keyword><style  face="normal" font="default" size="100%">valuation</style></keyword><keyword><style  face="normal" font="default" size="100%">Vasicek model</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">12/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/4/13.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">32</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;Utilizing the principle of balance between expected gain and expected&amp;nbsp;payment, this work obtains the analytic valuation formula for reverse mortgage. In&amp;nbsp;particular, we provide the formulas for the lump sum payment, joint annuity, increasing (decreasing) annuity, and level annuity of reverse mortgage. We also derive the&amp;nbsp;valuation equation that the variable payment annuities satisfy. We then discuss the&amp;nbsp;monotonicity of the lump sum, annuity, and annuity payment factors with respect to&amp;nbsp;the parameters associated with the home price and the interest rate model. Finally,&amp;nbsp;we analyze the sensitivity of the joint annuity with respect to the parameters associated with the home price, interest rate, and lifetime model. The numerical results&amp;nbsp;show that the average return of home price exerts a dominating influence on the joint&amp;nbsp;annuity, followed by the mean reversion level of interest rate, and both of them have&amp;nbsp;stronger impact on the annuities of younger applicants than those of older applicants.&amp;nbsp;Meanwhile, the initial age of male and that of female produce asymmetrical effect&amp;nbsp;on the joint annuity. Remarkably, the dependence of joint-lifetime significantly affect&amp;nbsp;the joint annuity value. In case that the male and female initial ages are both less&amp;nbsp;than 80 years old, annuity values on average increase&amp;nbsp; approximately 4.5%, and the&amp;nbsp;greatest increment of annuity value approaches 9%.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">895</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RAZIYE MERT</style></author><author><style face="normal" font="default" size="100%">LYNN ERBE</style></author><author><style face="normal" font="default" size="100%">THABET ABDELJAWAD</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A VARIATIONAL APPROACH OF THE STURM-LIOUVILLE PROBLEM IN FRACTIONAL DIFFERENCE CALCULUS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A08</style></keyword><keyword><style  face="normal" font="default" size="100%">35R11</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.acadsol.eu/dsa/articles/27/1/7.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this article, we formulate and analyze a nabla fractional difference Sturm Liouville problem (SLP) with the nabla left Caputo fractional difference&amp;nbsp;and the nabla right Riemann-Liouville fractional difference. The discrete fractional&amp;nbsp;variational calculus is used to study the eigenvalues and eigenfunctions of the formulated SLP by presenting a new nabla fractional difference isoperimetric variational&amp;nbsp;problem.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">137</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ELISA SOVRANO</style></author><author><style face="normal" font="default" size="100%">FABIO ZANOLIN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE AMBROSETTI-PRODI PERIODIC PROBLEM: DIFFERENT ROUTES TO COMPLEX DYNAMICS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C25</style></keyword><keyword><style  face="normal" font="default" size="100%">34C28</style></keyword><keyword><style  face="normal" font="default" size="100%">37G20</style></keyword><keyword><style  face="normal" font="default" size="100%">54H20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/34/13.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">38</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider a second order nonlinear ordinary differential equation of the form ${ u′′+ f(u) = p(t)}$&amp;nbsp; where the forcing term ${p(t)}$&amp;nbsp;is a ${T}$ -periodic function and the nonlinearity ${ f(u) }$ satisfies properties related to problems of Ambrosetti-Prodi type. We discuss the existence of infinitely many periodic solutions as well as the presence of complex dynamics under different conditions on ${ p(t) }$ and by using different kinds of approaches. On the one hand, we exploit the Melnikov’s method and, on the other hand, the concept of “topological horseshoe”.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3&amp;4</style></issue><section><style face="normal" font="default" size="100%">589</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DONGYA CHENG</style></author><author><style face="normal" font="default" size="100%">CHANGJUN YU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ASYMPTOTICS FOR THE RUIN PROBABILITIES OF A TWO-DIMENSIONAL RENEWAL RISK MODEL</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">62E10</style></keyword><keyword><style  face="normal" font="default" size="100%">62P05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/34/8.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we mainly consider the uniform asymptotic behavior for the finitetime ruin probabilities of a two-dimensional insurance model. In this model, the insurance company operates two classes of insurance business, whose claims occur in pairs and share a same claim arrival process. In the obtained result, the claim distributions cover most of the common subexponential distributions. The risk model with dependent inter-arrival times as well as the one with Brownian motion diffusions are also investigated.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3&amp;4</style></issue><section><style face="normal" font="default" size="100%">517</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">WATARU TAKAHASHI</style></author><author><style face="normal" font="default" size="100%">CHING-FENG WEN</style></author><author><style face="normal" font="default" size="100%">JEN-CHIH YAO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ATTRACTIVE AND MEAN CONVERGENCE THEOREMS FOR TWO COMMUTATIVE NONLINEAR MAPPINGS IN BANACH SPACES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H05</style></keyword><keyword><style  face="normal" font="default" size="100%">47H09</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/2/7.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">19</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, using the class of 2-generalized nonspreading mappings which was defined by [29] in a Banach space and covers 2-generalized hybrid mappings in a Hilbert space, we prove an attractive point theorem in a Banach space. Then we prove a mean convergence theorem of Baillon’s type [2] without convexity for commutative 2-generalized nonspreading mappings in a Banach space.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">327</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">VERA ZEIDAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">CONSTRAINED LINEAR-QUADRATIC CONTROL PROBLEMS OVER TIME SCALES AND WEAK NORMALITY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K35</style></keyword><keyword><style  face="normal" font="default" size="100%">39A12</style></keyword><keyword><style  face="normal" font="default" size="100%">49K15</style></keyword><keyword><style  face="normal" font="default" size="100%">49N25</style></keyword><keyword><style  face="normal" font="default" size="100%">93B05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/34/14.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">36</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;Time scale linear-quadratic control problems with affine mixed state-control and joint endpoints equality constraints are considered. Without any controllability assumption, it is shown that the feasible pairs at which the first variation vanishes are exactly the feasible pairs that satisfy the weak maximum principle (called &quot;extremals&quot;) with $\lambda_0 = 1$. In this case, we say the problem is &quot;weakly normal&quot; at such feasible pairs. When a certain matrix function $S(\cdot)$ has invertible images, the weak-normality condition at $(\bar x, \bar u)$ with associated adjoint variable $\bar p$ is also equivalent to $(\bar x, \bar p)$ solving the corresponding non-homogeneous symplectic boundary value problem and to $\bar u$ being a certain affine combination of this solution. In this equivalence, the invertibility of the corresponding matrices $S(t)$ is not needed when the linear-quadratic problem is itself symplectic. As an application, it is established that without any controllability assumption, the optimality in linear-quadratic problems is characterized in terms of either the weak normality condition, or the solvability of the corresponding symplectic boundary value. These results are obtained for linearquadratic control problems with or without shift in the state variable and are new not only for the time scale setting but also for the continuous time and discrete time settings.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3&amp;4</style></issue><section><style face="normal" font="default" size="100%">627</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BAPURAO  DHAGE</style></author><author><style face="normal" font="default" size="100%">SHYAM  DHAGE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">DHAGE ITERATION METHOD FOR GENERALIZED QUADRATIC FRACTIONAL INTEGRAL EQUATIONS WITH MAXIMA</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">45G10</style></keyword><keyword><style  face="normal" font="default" size="100%">47H09</style></keyword><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/34/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we prove an existence and an approximation result for a generalized nonlinear quadratic fractional integral equation with maxima of mixed type. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations starting with a lower or an upper solution converges monotonically to the solution of the related quadratic fractional integral equation with maxima under some suitable mixed hybrid conditions. We base our main results on the Dhage iteration principle embodied in a recent hybrid fixed point theorem of Dhage (2014) in a partially ordered normed linear space. A couple of numerical examples are also furnished to illustrate the hypotheses and abstract theory developed in the paper.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3&amp;4</style></issue><section><style face="normal" font="default" size="100%">435</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SHI’AN WANG</style></author><author><style face="normal" font="default" size="100%">N. AHMED</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">DYNAMIC MODEL OF URBAN TRAFFIC AND OPTIMUM MANAGEMENT OF ITS FLOW AND CONGESTION</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A50</style></keyword><keyword><style  face="normal" font="default" size="100%">93E20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/34/12.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we develop a dynamic model for urban traffic along with physical constraints characteristic of intersections equipped with traffic light. We introduce expressions for throughput and congestion and define an appropriate objective functional. Then we formulate an optimization problem whose solution if implemented is expected to reduce congestion and improve throughput. We use the principle of optimality to construct the optimization algorithm.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3&amp;4</style></issue><section><style face="normal" font="default" size="100%">575</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">F. BANDELE</style></author><author><style face="normal" font="default" size="100%">M. OGUNDIRAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE AND ASYMPTOTIC STABILITY OF AN IMPULSIVE STOCHASTIC DIFFERENTIAL EQUATION</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword><keyword><style  face="normal" font="default" size="100%">93E15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/1/1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we give necessary conditions for the existence and asymptotic stability of a mild solution for the impulsive stochastic differential equation. It is shown that the impulsive stochastic differential equation has a mild solution and the solution is asymptotically stable in the p-th moment.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">1</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ZEYNEP KAYAR</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">AN EXISTENCE AND UNIQUENESS RESULT FOR LINEAR SEQUENTIAL FRACTIONAL BOUNDARY VALUE PROBLEMS (BVPS) VIA LYAPUNOV TYPE INEQUALITY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A08</style></keyword><keyword><style  face="normal" font="default" size="100%">34B05</style></keyword><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/1/8.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A sufficient condition for the existence and uniqueness of solution of nonhomogenous fractional boundary value problem involving sequential fractional derivative of Riemann Liouville type is established by using a new Lyapunov type inequality and disconjugacy criterion. Green’s function and some of its properties are also presented. Our approach is quite new and to the best of our knowledge, the uniqueness of solution of nonhomogenous fractional boundary value problems is proved by employing Lyapunov type inequality for the first time and this Lyapunov type inequality improves and generalizes the previous ones.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">147</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">LINA MA</style></author><author><style face="normal" font="default" size="100%">JINGXIAO ZHANG</style></author><author><style face="normal" font="default" size="100%">D. KANNAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">FAIR PRICING OF REVERSE MORTGAGE WITHOUT REDEMPTION RIGHT</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/34/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">25</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We derive in this article the pricing of a reverse mortgage without redemption right. In this, the underlying model employs a jump-diffusion process to represent the dynamics of the housing price, the Vasicek model to drive the instantaneous interest rate, and the force mortality model to describe the longevity risk. The said pricing is based on the Principle of Balance between the expected gain and expected payment. We compute the expected gain and the expected payment respectively under the continuous and discrete framework. We also present, with the above model, explicit formulas for the increasing (or decreasing) perpetual annuity and the level perpetual annuity. Furthermore, we discuss the monotonicity property of the annuities, lump sum, and annuity payment factors with respect to the parameters associated with the house price, the interest rate, and the force of mortality model. Finally, some numerical results for the lump sum, the annuity, and the annuity payment factors are presented, and also the sensitivity with respect to the above parameters is discussed. Based on the average change rate, we evaluate all parameters’ degree of impact on the annuity, the lump sum, and the annuity payment factors.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3&amp;4</style></issue><section><style face="normal" font="default" size="100%">473</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ANUPAM SHARMA</style></author><author><style face="normal" font="default" size="100%">MOHAMMAD IMDAD</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">FIXED POINT APPROXIMATION OF GENERALIZED NONEXPANSIVE MULTI-VALUED MAPPINGS IN BANACH SPACES VIA NEW ITERATIVE ALGORITHMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H05</style></keyword><keyword><style  face="normal" font="default" size="100%">47H09</style></keyword><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/34/1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we introduce a new iterative algorithm to approximate the fixed points of generalized nonexpansive multi-valued mappings in Banach spaces and utilize the same to establish weak as well as strong convergence theorems. Our results generalize and improve several previously known results of the existing literature.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3&amp;4</style></issue><section><style face="normal" font="default" size="100%">395</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">EMMANUEL LEPINETTE</style></author><author><style face="normal" font="default" size="100%">FARSHID MEHRDOUST</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A FRACTIONAL VERSION OF THE HESTON MODEL WITH HURST PARAMETER H ∈ (1/2, 1)</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34F05</style></keyword><keyword><style  face="normal" font="default" size="100%">37H10</style></keyword><keyword><style  face="normal" font="default" size="100%">60H20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/34/9.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider a fractional version of the Heston model where the two standard Brownian motions are replaced by two fractional Brownian motions with Hurst parameter H ∈ (1/2, 1). We show that the stochastic differential equation admits a unique positive solution by adapting and generalizing some results of Y. Hu, D. Nualart and X. Song on singular equations driven by rough paths. Moreover, we show that the fractional version of the variance, which is a version of the fractional Cox-Ingersoll-Ross model, is still a mean-reverting process.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3&amp;4</style></issue><section><style face="normal" font="default" size="100%">537</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MARTIN  BOHNER</style></author><author><style face="normal" font="default" size="100%">MAHMOUD  OSMAN</style></author><author><style face="normal" font="default" size="100%">SAMIR  SAKER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">GENERAL HIGHER-ORDER DYNAMIC OPIAL INEQUALITIES WITH APPLICATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26D10</style></keyword><keyword><style  face="normal" font="default" size="100%">26D15</style></keyword><keyword><style  face="normal" font="default" size="100%">34A40</style></keyword><keyword><style  face="normal" font="default" size="100%">34N05</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A13</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/1/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we present some new generalizations of dynamic Opial-type inequalities of higher order on time scales. The results contain as special cases many of the results currently given in literature. As an application, we apply these inequalities together with a Hardy-type inequality on time scales to establish some lower bounds of the distance between zeros of a solution and/or its derivatives for a fourth-order dynamic equation.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">65</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DIEGO AVERNA</style></author><author><style face="normal" font="default" size="100%">GABRIELE BONANNO</style></author><author><style face="normal" font="default" size="100%">ELISABETTA TORNATORE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">GRADIENT NONLINEAR ELLIPTIC SYSTEMS DRIVEN BY A (p, q)-LAPLACIAN OPERATOR</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35J35</style></keyword><keyword><style  face="normal" font="default" size="100%">35J60</style></keyword><keyword><style  face="normal" font="default" size="100%">35J92</style></keyword><keyword><style  face="normal" font="default" size="100%">58E30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/2/9.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, using variational methods and critical point theorems, we prove the existence of multiple weak solutions for a gradient nonlinear Dirichlet elliptic system driven by a (p, q)-Laplacian operator.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">367</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ABOUBAKARY DIAKHABY</style></author><author><style face="normal" font="default" size="100%">YOUSSEF OUKNINE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">HOMOGENIZATION OF BSDES WITH TWO REFLECTING BARRIERS, VARIATIONAL INEQUALITY AND STOCHASTIC GAME</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">58E35</style></keyword><keyword><style  face="normal" font="default" size="100%">60G35</style></keyword><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/34/7.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we study the limit of semilinear variational inequality with bilateral constraints and stochastic differential games of mixed type. By a penalization method, we first study homogenization properties for system of two barriers reflected backward stochastic differential equation in the Markovian setting. This result together with certain techniques from stochastic calculus is then applied to show that the unique solution of the homogenized problem is also the value function of certain stochastic differential games of mixed type. Then using standard results from the theory of viscosity solutions, we show that the value function of this stochastic differential game with continuous control is the unique viscosity solution of the corresponding limit semilinear variational inequalities too.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3&amp;4</style></issue><section><style face="normal" font="default" size="100%">499</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JAN ANDRES</style></author><author><style face="normal" font="default" size="100%">LECH GORNIEWICZ</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">IMPLICIT DIFFERENTIAL INCLUSIONS WITH ACYCLIC RIGHT-HAND SIDES: AN ESSENTIAL FIXED POINTS APPROACH</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A09</style></keyword><keyword><style  face="normal" font="default" size="100%">34A60</style></keyword><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">54C60</style></keyword><keyword><style  face="normal" font="default" size="100%">55M20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/2/3.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">21</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Effective criteria are given for the solvability of initial as well as boundary value problems to implicit ordinary differential inclusions whose right-hand sides are governed by compact acyclic maps. Cauchy and periodic implicit problems are also considered on proximate retracts. Our new approach is based on the application of the topological essential fixed point theory. Implicit problems for partial differential inclusions are only indicated.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">237</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">N. MEDHIN</style></author><author><style face="normal" font="default" size="100%">M. SAMBANDHAM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">IMPULSIVE CONTROL PROBLEM GOVERNED BY FRACTIONAL DIFFERENTIAL EQUATIONS AND APPLICATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/1/3.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">27</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider an impulsive control problem governed by fractional differential equations for which we establish a set of necessary conditions. The results are applied to a model of an HIV-immune system with memory. The fact that fractional differential equations possess memory enhances their usefulness in the modeling effort. The objective of the control problem is to minimize the infectious viral load and count of infected CD4+T cells while using optimal level of dosage of anti-HIV drugs and optimal therapy. Simulation results are presented and discussed.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">37</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">TAHIRA JABEEN</style></author><author><style face="normal" font="default" size="100%">RAVI P. AGARWAL</style></author><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author><author><style face="normal" font="default" size="100%">VASILE LUPULESCU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS WITH CAUSAL OPERATORS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A37</style></keyword><keyword><style  face="normal" font="default" size="100%">34K05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/34/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we present an existence result for a class of impulsive differential equations with causal operators and prove that the solution set is compact in the space of regulated functions. The results are obtained under conditions with respect to the Hausdorff measure of noncompactness. An application from optimal control is given to illustrate our main result.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3&amp;4</style></issue><section><style face="normal" font="default" size="100%">411</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">E KORKMAZ</style></author><author><style face="normal" font="default" size="100%">C TUNC</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">INEQUALITIES AND EXPONENTIAL DECAY OF CERTAIN DIFFERENTIAL EQUATIONS OF FIRST ORDER IN TIME VARYING DELAY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C11</style></keyword><keyword><style  face="normal" font="default" size="100%">34D20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/1/9.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we give sufficient conditions to guarantee exponential decay of solutions to zero of the time varying delay differential equation of first order. By using the LyapunovKrasovskii functional approach, we establish new results on the exponential decay of solutions, which include and improve some related results in the literature.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">157</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">KHANLAR  MAMEDOV</style></author><author><style face="normal" font="default" size="100%">OZGE AKCAY</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">INVERSE PROBLEM FOR A CLASS OF DIRAC OPERATORS BY THE WEYL FUNCTION</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A55</style></keyword><keyword><style  face="normal" font="default" size="100%">34L10</style></keyword><keyword><style  face="normal" font="default" size="100%">34L40</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/1/11.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">1</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper is related to an inverse problem for a class of Dirac operators with discontinuous coefficient and eigenvalue parameter contained in boundary conditions. The asymptotic formula of eigenvalues of this problem is examined. Weyl solution and Weyl function are constructed. Uniqueness theorem of the inverse problem respect to the Weyl function is proved.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">183</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">KRASNOSELSKII COINCIDENCE TYPE RESULTS FOR GENERAL CLASSES OF MAPS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H04</style></keyword><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/34/3.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper coincidence type results for general classes of maps are presented. A variety of different situations are discussed.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3&amp;4</style></issue><section><style face="normal" font="default" size="100%">425</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">LIMIT OF INVERSE SYSTEMS AND COINCIDENCE PRINCIPLES IN FRECHET SPACE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword><keyword><style  face="normal" font="default" size="100%">54H25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/2/10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Using the notion of Φ-essential or Φ-epi maps we present a variety of coincidence principles for multimaps defined on subsets of Fr´echet spaces.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">383</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ELHAM DASTRANJ</style></author><author><style face="normal" font="default" size="100%">SHIVA NAMAZI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">LOCAL RISK MINIMIZING OPTION IN A REGIME-SWITCHING DOUBLE HESTON MODEL</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">80G91</style></keyword><keyword><style  face="normal" font="default" size="100%">91G60</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/34/11.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We address risk minimizing option pricing in a regime switching double Heston model with three jumps when the underlying asset price follows a general state-dependent regimeswitching jump-diffusion process. Using minimal martingale measure, an optimal hedging strategy is obtained by the local risk minimization.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3&amp;4</style></issue><section><style face="normal" font="default" size="100%">563</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RAVI AGARWAL</style></author><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author><author><style face="normal" font="default" size="100%">SNEZHANA HRISTOVA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MONOTONE-ITERATIVE TECHNIQUES FOR MILD SOLUTIONS OF THE INITIAL VALUE PROBLEM FOR CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-INSTANTANEOUS IMPULSES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A37</style></keyword><keyword><style  face="normal" font="default" size="100%">34E08</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/2/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">26</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The main aim of the paper is to suggest some algorithms to approximately solve the initial value problem for scalar nonlinear Caputo fractional differential equations with noninstantaneous impulses. The impulses start abruptly at some points and their action continue on given finite intervals. We study the case when the right hand side of the equations are monotonic functions. Several types of mild lower and mild upper solutions to the problem are defined and used in the algorithms. The convergence of the successive approximations is established. A generalization of the logistic equation is given to illustrate the results.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">211</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">LESZEK GASINSKI</style></author><author><style face="normal" font="default" size="100%">NIKOLAOS  PAPAGEORGIOU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">PAIRS OF NONTRIVIAL SOLUTIONS FOR RESONANT ROBIN PROBLEMS WITH INDEFINITE LINEAR PART</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35J20</style></keyword><keyword><style  face="normal" font="default" size="100%">35J60</style></keyword><keyword><style  face="normal" font="default" size="100%">58E05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/2/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential and a Carath´eodory reaction term which exhibits linear growth near ±∞ and near zero. Resonance with respect to different eigenvalues can occur at both ±∞ and near zero. Using the saddle point reduction method and Morse theory (critical groups), we prove a multiplicity theorem producing two nontrivial smooth solutions.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">309</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MALIK MUSLIM</style></author><author><style face="normal" font="default" size="100%">AVADHESH KUMAR</style></author><author><style face="normal" font="default" size="100%">MICHAL FEÇKAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">PERIODIC SOLUTIONS TO SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH NON-INSTANTANEOUS IMPULSES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34G20</style></keyword><keyword><style  face="normal" font="default" size="100%">34K30</style></keyword><keyword><style  face="normal" font="default" size="100%">34K45</style></keyword><keyword><style  face="normal" font="default" size="100%">47D09</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/2/1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we consider a non-instantaneous impulsive system represented by the second order nonlinear differential equations in a Banach space. We use the strongly continuous cosine family of linear operators along with Schauder and Banach fixed point theorems to study the existence and uniqueness of the periodic solutions of the non-instantaneous impulsive system. Moreover, we construct a Poincar´e operator, which is a composition of the maps and we apply the techniques of a priori estimate for this operator. Finally, we give an example to illustrate the application of these obtained abstract results.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">197</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">LINA MA</style></author><author><style face="normal" font="default" size="100%">JINGXIAO ZHANG</style></author><author><style face="normal" font="default" size="100%">D. KANNAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">PRICING AN INSURANCE PRODUCT THAT INTEGRATES REVERSE MORTGAGE WITH LONG-TERM CARE INSURANCE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/1/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">25</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We derive in this article the pricing formula for an insurance product that integrates reverse mortgage with long term care. This pricing is based on the principle of balance between the mean gain and mean payment. We compute the expected gain and the expected payment respectively under the continuous and discrete framework. Here, we assume that the dynamics of the housing price is driven by the Black-Scholes model and the interest rate is driven by the Ornstein-Uhlenbeck process. With these assumptions, we present closed-form formulas for the growing perpetuity annuity, the state annuity, and the constant annuity. Furthermore, we discuss the monotonicity property of the annuities, lump sum, and annuity payment factors with respect to the parameters of housing price, interest rate model, and the age of the insured. We present the numerical results for the lump sum, the annuity, and the annuity payment factors, and analyze the sensitivity with respect to the above parameters. We also show that the mean return of housing price has the dominating influence on the lump sum and annuity&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">11</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">KENZU ABDELLA</style></author><author><style face="normal" font="default" size="100%">GLEN ROSS</style></author><author><style face="normal" font="default" size="100%">YASAMAN MOHSENIAHOUEI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOLUTIONS TO THE BLASIUS AND SAKIADIS PROBLEMS VIA A NEW SINC-COLLOCATION APPROACH</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">65L10</style></keyword><keyword><style  face="normal" font="default" size="100%">65Z05</style></keyword><keyword><style  face="normal" font="default" size="100%">76D10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/1/5.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Two well-known nonlinear laminar boundary layer problems, the Blasius and the Sakiadis problems, are treated by a new Sinc-Collocation approach based on first derivative interpolation. Even in the presence of singularities or infinite domains, the Sinc-Collocation method is known to exhibit exponential convergence, resulting in highly accurate solutions. The new method is suggested over the customary Sinc approaches due to decreased sensitivity to numerical errors. It is shown that this approach is an accurate and efficient tool in solving these nonlinear boundary value problems.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">105</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">NESLIHAN  PELEN</style></author><author><style face="normal" font="default" size="100%">AYSE  GUVENILIR</style></author><author><style face="normal" font="default" size="100%">BILLUR KAYMAKÇALAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOME RESULTS ON PREDATOR-PREY DYNAMIC SYSTEMS WITH BEDDINGTON-DEANGELIS TYPE FUNCTIONAL RESPONSE ON TIME SCALE CALCULUS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/1/10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider two dimensional predator-prey system with Beddington-DeAngelis type functional response on time scales. For this special case, we try to find under which conditions the system is permanent and globally attractive. This study gives beneficial results for continuous and discrete cases and also for solving open problems related to the dynamical properties of the systems which include the species that have unusual life cycle.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">167</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Cemil Tunc</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STABILITY AND BOUNDEDNESS IN VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH DELAY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34D05</style></keyword><keyword><style  face="normal" font="default" size="100%">34K20</style></keyword><keyword><style  face="normal" font="default" size="100%">45J05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/1/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, a class of non-linear vector Volterra integro-differential equations of first order with constant delay is considered. The stability and boundedness of solutions are investigated. The technique of proofs involves defining appropriate Lyapunov functionals. The obtained results include and improve the results obtained in literature.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">121</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ELENA BRAVERMAN</style></author><author><style face="normal" font="default" size="100%">MICHELLE MICHELLE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STABILITY OF TIME-DEPENDENT DYNAMIC MONOPOLY WITH CONCENTRATED AND DISTRIBUTED DELAYS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K20</style></keyword><keyword><style  face="normal" font="default" size="100%">91B55</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/2/8.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">19</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A possible combination of continuously distributed and concentrated delays is incorporated in a monopoly model with either bounded or unbounded time window for the past data, while its length and the adjustment speed may vary. In this general setting, we obtain sufficient stability conditions. Sharper tests are established for autonomous equations with finite or infinite distributed delays. A similar stability analysis is implemented for the output of the leader firm in the Stackelberg duopoly model.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">347</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">KRISTINA HILTON</style></author><author><style face="normal" font="default" size="100%">G. LADDE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STOCHASTIC MULTICULTURAL DYNAMIC NETWORKS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">37H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/34/5.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">19</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this work, we seek to study the cohesive properties of a dynamic multi-cultural network under random environmental perturbations. By considering a multi-agent dynamic network, we seek to model a social structure and find conditions under which cohesion and coexistence is maintained. Utilizing Lyapunov’s Second Method and the comparison method, we present a prototype illustration which serves the significance of the framework and approach. Moreover, the explicit sufficient conditions in terms of system parameters are given to exhibit when the network is cohesive. The sufficient conditions are algebraically simple, easy to verify, and robust. Further, we decompose the cultural state domain into invariant sets and consider the behavior of members within each set. We also demonstrate how conservative the estimates are using Euler-Maruyama type numerical approximation schemes based on the given illustration.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3&amp;4</style></issue><section><style face="normal" font="default" size="100%">453</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MARTIN BOHNER</style></author><author><style face="normal" font="default" size="100%">GIUSEPPE CARISTI</style></author><author><style face="normal" font="default" size="100%">SHAPOUR HEIDARKHANI</style></author><author><style face="normal" font="default" size="100%">AMJAD SALARI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THREE SOLUTIONS FOR A CLASS OF NONHOMOGENEOUS NONLOCAL SYSTEMS: AN ORLICZ-SOBOLEV SPACE SETTING</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35J60</style></keyword><keyword><style  face="normal" font="default" size="100%">35J70</style></keyword><keyword><style  face="normal" font="default" size="100%">46E35</style></keyword><keyword><style  face="normal" font="default" size="100%">58E05</style></keyword><keyword><style  face="normal" font="default" size="100%">68T40</style></keyword><keyword><style  face="normal" font="default" size="100%">76A02</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/2/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">24</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this work, we investigate the existence of multiple solutions for a class of nonhomogeneous nonlocal systems via variational methods and critical point theory. We give a new criteria for guaranteeing that the nonhomogeneous nonlocal systems with a perturbed term have at least three solutions in an appropriate Orlicz-Sobolev space. By presenting two examples we illustrate the results.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">259</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">TOPOLOGICAL STRUCTURE OF THE COINCIDENCE SET FOR ABSTRACT CLASSES OF MAPS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">54H25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/34/10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The existence of a coincidence point is discussed in an abstract setting. In addition we consider the case when the coincidence set contains a continuum intersecting a given set.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3&amp;4</style></issue><section><style face="normal" font="default" size="100%">549</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SEHIE PARK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON VARIOUS MULTIMAP CLASSES IN THE KKM THEORY AND THEIR APPLICATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H04</style></keyword><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword><keyword><style  face="normal" font="default" size="100%">47J20</style></keyword><keyword><style  face="normal" font="default" size="100%">47N10</style></keyword><keyword><style  face="normal" font="default" size="100%">49J53</style></keyword><keyword><style  face="normal" font="default" size="100%">52A99</style></keyword><keyword><style  face="normal" font="default" size="100%">54C60</style></keyword><keyword><style  face="normal" font="default" size="100%">54H25</style></keyword><keyword><style  face="normal" font="default" size="100%">58E35</style></keyword><keyword><style  face="normal" font="default" size="100%">90C47</style></keyword><keyword><style  face="normal" font="default" size="100%">91A13</style></keyword><keyword><style  face="normal" font="default" size="100%">91B50</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/2/5.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">26</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Fixed point theory of convex-valued multimaps are closely related to the KKM theory from the beginning. In the last twenty-five years, we introduced the acyclic multimap class, the admissible multimap class &lt;em&gt;A&lt;sup&gt;κ&lt;/sup&gt;&lt;sub&gt;c&lt;/sub&gt; &lt;/em&gt;, the better admissible class &lt;em&gt;B&lt;/em&gt;, and the KKM admissible classes &lt;em&gt;KC&lt;/em&gt;, &lt;em&gt;KO&lt;/em&gt; in the frame of the KKM theory. Our aim in this review is to collect the basic properties of our multimap classes and some mutual relations among them in general topological spaces or our abstract convex spaces. We add some new remarks and further comments to improve many of those results, and introduce some recent applications of our multimap classes.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">283</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MARAT AKHMET</style></author><author><style face="normal" font="default" size="100%">AYSEGUL KIVILCIM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">VERTICAL AND HORIZONTAL GRAZING</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A37</style></keyword><keyword><style  face="normal" font="default" size="100%">34C25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/1/7.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Grazing solutions of non-autonomous system with variable moments of impulses are examined. Appropriate denitions for vertial and horizontal grazing in non-autonomous systems are given and interpreted geometrially. The linearization for the periodi solutions whih have vertial or horizontal grazing is obtained. Examples are presented to demonstrate the pratiality of our results and they are visualized by the simulations.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">131</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">John R. Graef</style></author></authors><secondary-authors><author><style face="normal" font="default" size="100%">Cemil Tunc</style></author><author><style face="normal" font="default" size="100%">Sebaheddin Sevgin</style></author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">BEHAVIOR OF SOLUTIONS OF NONLINEAR FUNCTIONAL VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH MULTIPLE DELAYS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K12 34K20</style></keyword><keyword><style  face="normal" font="default" size="100%">45D05</style></keyword><keyword><style  face="normal" font="default" size="100%">45M10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.acadsol.eu/dsa/articles/25/3.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;The authors consider the nonlinear functional Volterra integro-differential equation with multiple delays&lt;/p&gt;

&lt;p&gt;$$ x^{\prime}(t) = - a(t)x(t) + \sum_{i=1}^n \int_{t-\tau_i}^{t} b_i(t,s)f_i(x(s))ds. $$&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;They give sufficient conditions so that solutions are bounded, belong to $L^1$, or belong to $L^2$. They also prove the stability and global asymptotic stability of the zero solution. Their technique of proof involves defining appropriate Lyapunov functionals.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">39</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">VELI B. SHAKHMUROV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE CAUCHY PROBLEM FOR GENERALIZED ABSTRACT BOUSSINESQ EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35Lxx</style></keyword><keyword><style  face="normal" font="default" size="100%">35Qxx</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">43Axx</style></keyword><keyword><style  face="normal" font="default" size="100%">47Axx</style></keyword><keyword><style  face="normal" font="default" size="100%">47Hxx</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.acadsol.eu/dsa/articles/25/8.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, the existence and uniqueness of solution of the Cauchy problem for abstract Boussinesq equations is obtained. By applying this result, the Wentzell-Robin type mixed problem for Boussinesq equations and the Cauchy problem for finite or infinite systems of Boussinesq equations are studied.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">109</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ÖZKAN ÖZTÜRK</style></author><author><style face="normal" font="default" size="100%">ELVAN AKIN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">CLASSIFICATION OF NONOSCILLATORY SOLUTIONS OF NONLINEAR DYNAMIC EQUATIONS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.acadsol.eu/dsa/articles/25/13.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study the asymptotic behavior of nonoscillatory solutions of nonlinear dynamic equations on time scales. More precisely, all eventually monotone solutions of nonlinear dynamic equations can be divided into several disjoint subsets by means of necessary and sufficient integral conditions. Examples are given to illustrate some of our main results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">219</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MARIN MARIN</style></author><author><style face="normal" font="default" size="100%">EDUARD-MARIUS CRACIUN</style></author><author><style face="normal" font="default" size="100%">NICOLAE POP</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">CONSIDERATIONS ON MIXED INITIAL-BOUNDARY VALUE PROBLEMS FOR MICOPOLAR POROUS BODIES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35B35</style></keyword><keyword><style  face="normal" font="default" size="100%">47D05</style></keyword><keyword><style  face="normal" font="default" size="100%">74A15</style></keyword><keyword><style  face="normal" font="default" size="100%">74A60.</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.acadsol.eu/dsa/articles/25/11.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">21</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper is dedicated to some results in the thermodynamic theory of porous elastic bodies. Unlike other studies, here is included the voidage time derivative among the independent constitutive variables. In order to analyse the spatial behavior of solutions, we use some estimates of Saint-Venant type in the case of bounded bodies, while for the unbounded bodies, the spatial behavior is described by means of some estimates of Phragm´en-Lindel¨of type.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">175</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">EMAN ALAIDAROUS</style></author><author><style face="normal" font="default" size="100%">AMEL BENAISSA</style></author><author><style face="normal" font="default" size="100%">MOUFFAK BENCHOHRA</style></author><author><style face="normal" font="default" size="100%">JOHNNY HENDERSON</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">GLOBAL EXISTENCE RESULTS FOR FUNCTIONAL EVOLUTION EQUATIONS WITH DELAY AND RANDOM EFFECTS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34G20</style></keyword><keyword><style  face="normal" font="default" size="100%">34K20</style></keyword><keyword><style  face="normal" font="default" size="100%">34K30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.acadsol.eu/dsa/articles/25/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study the existence of mild solutions of a functional evolution equation with infinite delay and random effects. We use a random fixed point theorem with stochastic domain.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">89</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ABDOLLAH NAZARI</style></author><author><style face="normal" font="default" size="100%">GHASEM A. AFROUZI</style></author><author><style face="normal" font="default" size="100%">SHAPOUR HEIDARKHANI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">INFINITELY MANY SOLUTIONS FOR PERTURBED FOURTH-ORDER KIRCHHOFF-TYPE PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">58E05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.acadsol.eu/dsa/articles/25/14.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Existence results of infinitely many solutions for perturbed fourth-order Kirchhoff- type problems are established. No symmetric condition on the nonlinear term is assumed. The main tool is an infinitely many critical points theorem&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">273</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">LERAY-SCHAUDER AND FURI-PERA TYPE RESULTS BASED ON Φ-EPI MAPS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H04</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.acadsol.eu/dsa/articles/25/7.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper using the notion of Φ-epi maps we present new and abstract LeraySchauder and Furi-Pera type results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">101</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JIA BAOGUO</style></author><author><style face="normal" font="default" size="100%">LYNN ERBE</style></author><author><style face="normal" font="default" size="100%">ALLAN PETERSON</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MONOTONICITY AND CONVEXITY FOR NABLA FRACTIONAL q-DIFFERENCES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications </style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">26A48</style></keyword><keyword><style  face="normal" font="default" size="100%">39A70</style></keyword><keyword><style  face="normal" font="default" size="100%">39A99.</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.acadsol.eu/dsa/articles/25/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper, we examine the relation between monotonicity and convexity for nabla fractional q-differences. In particular we prove that&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Theorem A. &lt;/strong&gt;Assume $f : q^{N_0} \longrightarrow R$, $\nabla^{\nu}_q f(t) ≥ 0$ for each $t \in&amp;nbsp;q^{N_0}$, with $1 &amp;lt; \nu&amp;nbsp;&amp;lt; 2$, then $\nabla_q f(t) \geq&amp;nbsp;0$ for $t\in q^{N_1}$.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Theorem B.&lt;/strong&gt; Assume $f : q^{N_0} \longrightarrow R$, $\nabla^{\nu}_q f(t) ≥ 0$ for each $t \in&amp;nbsp;q^{N_1}$, with $2&amp;nbsp;&amp;lt; \nu&amp;nbsp;&amp;lt; 3$, then $\nabla_q^2 f(t) \geq&amp;nbsp;0$ for $t\in q^{N_2}$.&lt;/p&gt;

&lt;p&gt;This shows that, in some sense, the positivity of the $\mu$-th order $q$-fractional difference has a strong connection to the monotonicity and convexity of $f(t)$.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%"> 47</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SMAIL DJEBALI</style></author><author><style face="normal" font="default" size="100%">KARIMA MEBARK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SINGULAR SEMI-POSITONE φ-LAPLACIAN BVP ON INFINITE INTERVAL IN BANACH SPACES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">34b18</style></keyword><keyword><style  face="normal" font="default" size="100%">34B40</style></keyword><keyword><style  face="normal" font="default" size="100%">47H07</style></keyword><keyword><style  face="normal" font="default" size="100%">47H08</style></keyword><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.acadsol.eu/dsa/articles/25/12.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">21</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this work, we have obtained new existence results of unbounded positive solutions for a second-order φ-Laplacian equation subject to nonlinear integral boundary conditions of Riemann-Stieltjes type and posed on the positive half-line. The index fixed point theory on cones of Banach spaces for countably strict set-contractions has been employed. The nonlinearity depends on the solution and its derivative, may change sign, and has time and space singularities in its arguments. It further takes values in a general Banach space and is assumed to have quite general growth conditions. We have illustrated our theoretical results with two examples of application in a finite and in an infinite dimensional space, respectively.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">197</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">KY QUAN TRAN</style></author><author><style face="normal" font="default" size="100%">G. YIN</style></author><author><style face="normal" font="default" size="100%">LE YI WANG</style></author><author><style face="normal" font="default" size="100%">HANQIN ZHANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SINGULARLY PERTURBED MULTI-SCALE SWITCHING DIFFUSIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35C20</style></keyword><keyword><style  face="normal" font="default" size="100%">35K45</style></keyword><keyword><style  face="normal" font="default" size="100%">60J35</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.acadsol.eu/dsa/articles/25/10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">21</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This work is concerned with singularly perturbed multi-scale switching diffusions. The switching process is a two-time-scale Markov chain with slow and fast components subject to weak and strong interactions. In the model, there are two small parameters ε and δ. The first one highlights the fast changing part of the switching process, and the other delineates the slow diffusion. We treat the case that ε and δ are related in that ε = δ γ . Under certain conditions, asymptotic expansions of the probability densities for the underlying processes are developed. The approach is constructive and the asymptotic series are rigorously justified with error bounds.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">153</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Yelda Aygar</style></author><author><style face="normal" font="default" size="100%">Martin J. Bohner</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SPECTRAL ANALYSIS OF A MATRIX-VALUED QUANTUM-DIFFERENCE OPERATOR</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications </style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;The aim of this work is to find a polynomial-type Jost solution of a self adjoint matrix-valued q-difference equation of second order and investigate the spectral properties of the operator L generated by this q-difference expression by using asymptotic behavior of the Jost solution&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">29</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MOUATAZ BILLAH MESMOULI</style></author><author><style face="normal" font="default" size="100%">ABDELOUAHEB ARDJOUNI</style></author><author><style face="normal" font="default" size="100%">AHCENE DJOUDI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STABILITY SOLUTIONS FOR A SYSTEM OF NONLINEAR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH FUNCTIONAL DELAY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A34</style></keyword><keyword><style  face="normal" font="default" size="100%">34K20</style></keyword><keyword><style  face="normal" font="default" size="100%">34K40</style></keyword><keyword><style  face="normal" font="default" size="100%">35A08</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.acadsol.eu/dsa/articles/25/15.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we use the fixed point theorem to obtain stability results of the zero solution of a nonlinear neutral system of differential equations with functional delay. Application to the second-order model is given with an example.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">253</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MACIEJ KOZARYN</style></author><author><style face="normal" font="default" size="100%">MARIUSZ MICHTA</style></author><author><style face="normal" font="default" size="100%">KAMIL Ł. ŚWIĄTEK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STOCHASTIC INCLUSIONS DRIVEN BY TWO-PARAMETER MARTINGALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Random Field</style></keyword><keyword><style  face="normal" font="default" size="100%">Set-valued Stochastic Integral Equation</style></keyword><keyword><style  face="normal" font="default" size="100%">Stochastic Inclusion</style></keyword><keyword><style  face="normal" font="default" size="100%">Two-parameter martingale</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.acadsol.eu/dsa/articles/25/9.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">30</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The aim of the paper is the analysis of existence and properties of solutions to stochastic integral inclusions driven by two-parameter martingales. In our investigations we apply set-valued stochastic integral equations and we establish their connections with stochastic integral inclusions. Finally, we show how some particular two-parameter stochastic models are related to stochastic inclusions.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">123</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">N. U. AHMED</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SYSTEMS GOVERNED BY MEAN-FIELD STOCHASTIC EVOLUTION EQUATIONS ON HILBERT SPACES AND THEIR OPTIMAL CONTROL</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Existence of Optimal Controls</style></keyword><keyword><style  face="normal" font="default" size="100%">Hilbert Spaces</style></keyword><keyword><style  face="normal" font="default" size="100%">McKean-Vlasov mean-field Stochastic Differential Equation</style></keyword><keyword><style  face="normal" font="default" size="100%">Necessary conditions of optimality.</style></keyword><keyword><style  face="normal" font="default" size="100%">Relaxed Controls</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.acadsol.eu/dsa/articles/25/5.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">27</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we consider a general class of controlled McKean-Vlasov mean-field stochastic evolution equations on Hilbert spaces. We prove existence, uniqueness and regularity properties of mild solutions of these equations. Relaxed controls, covering regular controls, adapted to a current of sub-sigma algebras generated by observable processes and taking values from a Polish space, are used. An appropriate metric topology, based on weak star convergence, is introduced. We prove continuous dependence of solutions on controls with respect to this topology. These results are then used to prove existence of optimal controls for Bolza problem. Then we develop the necessary conditions of optimality using semi-martingale representation theory and show that the adjoint processes arising from the necessary conditions can be constructed from the mild solution of certain backward stochastic mean field evolution equation (BSMEE). The paper is concluded with some applications to mean-field linear quadratic regulator problems.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">61</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">CHAO WANG</style></author><author><style face="normal" font="default" size="100%">RAVI P. AGARWAL</style></author><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Π-SEMIGROUP FOR INVARIANT UNDER TRANSLATIONS TIME SCALES AND ABSTRACT WEIGHTED PSEUDO ALMOST PERIODIC FUNCTIONS WITH APPLICATIONS</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper, we introduce and discuss the concept of a Π-semigroup for invariant under translations time scales and the concept of abstract weighted pseudo almost periodic functions in Banach spaces. As an application, we obtain conditions for the existence of weighted pseudo almost periodic solutions for a class of neutral functional differential equations on time scales&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BEHZAD DJAFARI ROUHANI</style></author><author><style face="normal" font="default" size="100%">HADI KHATIBZADEH</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ASYMPTOTIC BEHAVIOR FOR A GENERAL CLASS OF HOMOGENEOUS SECOND ORDER EVOLUTION EQUATIONS IN A HILBERT SPACE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A23</style></keyword><keyword><style  face="normal" font="default" size="100%">47H05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/01-dsa-01-16.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study the asymptotic behavior of solutions to the following general homogeneous second order evolution equation, with suitable assumptions on $p(t)$ and $r(t)$,&lt;/p&gt;

&lt;p&gt;$$ \left\{\begin{array}{ll} p(t)u^{\prime\prime}(t) + r(t)u^{\prime}(t) \in Au(t) &amp;amp; \text{a.e. on}\ R^+,\\ u(0) = u_0, &amp;amp; \sup_{t\geq 0} |u(t)| &amp;lt; +\infty, \end{array} \right.$$&lt;/p&gt;

&lt;p&gt;where $A$ is a maximal monotone operator in a real Hilbert space, and present some applications. In the homogeneous case, our results extend those given in [7, 10, 12].&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">1</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. B. KHAN</style></author><author><style face="normal" font="default" size="100%">N. U. AHMED</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">AN ATTEMPT TOWARDS DYNAMIC MODELING OF THE EARTH’S CLIMATE SYSTEM</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35K51</style></keyword><keyword><style  face="normal" font="default" size="100%">35K55</style></keyword><keyword><style  face="normal" font="default" size="100%">76N99</style></keyword><keyword><style  face="normal" font="default" size="100%">93C20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/12-dsa-155-168.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we attempt to develop a broader dynamic (mathematical) model for the climate system of the planet earth. This is based on two major components namely the atmosphere around the planet and the oceans all subject to the solar radiation, lunar gravity and their impact on land, sea and the atmosphere. It is assumed that the atmosphere-ocean interaction is the fundamental source of the global climate variability. Based on this fact we develop a mathematical model that takes into account all the possible major interactions. This model is further extended to a stochastic dynamic system in order to include uncertainties in many of the natural forces. The authors believe that this model will allow for numerical evaluation of many physical variables of interest possibly leading to a better understanding of the climate variability of the earth as a whole.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">155</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">HAMED H. ALSULAMI</style></author><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">COINCIDENCE POINTS FOR MULTIMAPS DEFINED ON SUBSETS OF FRÉCHET SPACES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H04</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/17-dsa-221-228.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We establish coincidence points for maps defined on Fr´echet spaces. The proofs rely on the notion of a Φ-essential map and on viewing the Fr´echet space as the projective limit of a sequence of Banach spaces.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">221</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">COINCIDENCE POINTS FOR MULTIVALUED MAPS BASED ON Φ-EPI AND Φ-ESSENTIAL MAPS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H04</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/11-dsa-143-154.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Two approaches to establishing coincidence points for general classes of maps are presented. The first is based on the notion of a Φ-epi map and the second is based on the notion of a Φ-essential map.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">143</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">NGUYEN  HA</style></author><author><style face="normal" font="default" size="100%">NGUYEN DU</style></author><author><style face="normal" font="default" size="100%">DO  THUAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE CONVERGENCE OF SOLUTIONS TO NABLA DYNAMIC EQUATIONS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">06B99</style></keyword><keyword><style  face="normal" font="default" size="100%">34D99</style></keyword><keyword><style  face="normal" font="default" size="100%">47A10</style></keyword><keyword><style  face="normal" font="default" size="100%">47A99</style></keyword><keyword><style  face="normal" font="default" size="100%">65P99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/36-DSA-451-466.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper deals with the convergence of solutions to nabla dynamic equations x &lt;sup&gt;∇&lt;/sup&gt; = f (t, x) on time scales {Tn}&lt;sup&gt;∞&lt;/sup&gt;&lt;sub&gt;n=1&lt;/sub&gt; when this sequence converges to the time scale T. The convergent rate of solutions is evaluated when f satisfies the Lipschitz condition in both variables. A new approach to the approximation of dynamic equations on time scales is derived by a general view, especially the implicit Euler method for differential equations. Some examples are given to illustrate results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">451</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">EMIN OZYILMAZ</style></author><author><style face="normal" font="default" size="100%">YUSUF YAYLI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE DIFFERENTIAL GEOMETRY OF REGULAR CURVES ON A REGULAR TIME-LIKE SURFACE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">53A04</style></keyword><keyword><style  face="normal" font="default" size="100%">53B30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/28-DSA-349-360.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this study, we consider time-like regular surface in Minkowski space as y = y(u, v) and investigate Darboux vectors of the time-like curves on time-like surface as (c), (c&lt;sub&gt;1&lt;/sub&gt;) and (c&lt;sub&gt;2&lt;/sub&gt;) which are not intersect perpendicularly. Moreover, we give a relation between the Darboux vectors of these Darboux frames. By this relation we obtain general Liouville formula and general form Euler and O. Bonnet.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">349</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author><author><style face="normal" font="default" size="100%">ALEKSANDRA ORPEL</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EIGENVALUE PROBLEM FOR ODES WITH A PERTURBED Q-LAPLACE OPERATOR</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B16</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/07-dsa-97-112.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We investigate the eigenvalue interval for boundary value problem with a onedimensional perturbed q-Laplace operator. Our results cover also the case when the right-hand side has singularities. Applying variational methods we prove the existence of positive solutions and establish their continuous dependence on functional parameters.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">97</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">UMMAHAN AKCAN</style></author><author><style face="normal" font="default" size="100%">NUKET AYKUT HAMAL</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE AND MONOTONE ITERATION OF CONCAVE POSITIVE SYMMETRIC SOLUTIONS FOR A THREE-POINT SECOND-ORDER BOUNDARY VALUE PROBLEMS WITH INTEGRAL BOUNDARY CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">39B18</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/20-DSA-259-270.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this article, we make use of the monotone iterative technique to verify the existence of concave symmetric positive solutions of a second-order three-point boundary value problem with integral boundary conditions. The interesting point here is that the nonlinear term f depends on the first-order derivative explicitly. An example which supports our result is also indicated.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">259</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ABDULKADIR DOGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE EXISTENCE OF POSITIVE SOLUTIONS FOR A SEMIPOSITONE SECOND-ORDER m-POINT BOUNDARY VALUE PROBLEM</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">34b18</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/33-DSA-419-428.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we study the existence of positive solutions to boundary value problem&lt;/p&gt;

&lt;p&gt;$$ \left\{\begin{array}{ll} u^{\prime\prime} + \lambda f(t,u) = 0, &amp;amp; t \in (0, 1),\\ u(0) = \sum_{i=1}^{m-2}\alpha_i u(\xi_i), &amp;amp; u^{\prime}(1) = \sum_{i=1}^{m-2}\beta_i u^{\prime}(\xi_i), \end{array} \right. $$&lt;/p&gt;

&lt;p&gt;where $\xi_i \in&amp;nbsp;(0, 1)$, $0 &amp;lt; \xi_1 &amp;lt; \xi_2 &amp;lt;\cdots&amp;nbsp;&amp;lt; \xi_{m−2} &amp;lt; 1$, $\alpha_i , \beta_i \in&amp;nbsp;[0, ∞)$, $λ$ is positive parameter. By using Krasnosel’skii’s fixed point theorem, we provide sufficient conditions for the existence of at least one positive solution to the above boundary value problem.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">419</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ABDULKADIR DOGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE EXISTENCE OF POSITIVE SOLUTIONS FOR THE ONE-DIMENSIONAL p-LAPLACIAN BOUNDARY VALUE PROBLEMS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">34B16</style></keyword><keyword><style  face="normal" font="default" size="100%">34b18</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/23-DSA-295-304.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we study the following p-Laplacian boundary value problems on time scales ( (φp(u ∆(t)))∇ + a(t)f(t, u(t), u∆(t)) = 0, t ∈ [0, T ]T, u(0) − B0(u ∆(0)) = 0, u∆(T ) = 0, where φp(u) = |u| p−2u, for p &amp;gt; 1. We prove the existence of triple positive solutions for the onedimensional p-Laplacian boundary value problem by using the Leggett-Williams fixed point theorem. The interesting point in this paper is that the non-linear term f is involved with first-order derivative explicitly. An example is also given to illustrate the main result.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">295</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">TUGBA SENLIK CERDIK</style></author><author><style face="normal" font="default" size="100%">NUKET AYKUT HAMAL</style></author><author><style face="normal" font="default" size="100%">FULYA YORUK DEREN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH m-POINT INTEGRAL BOUNDARY CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/22-DSA-283-294.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we consider m-point integral boundary value problems for fractional differential equations involving the Riemann Liouville fractional derivative. The existence results of solutions are established via the application of fixed point theorem.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">283</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">M. BELMEKKI</style></author><author><style face="normal" font="default" size="100%">S. K. NTOUYAS</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE RESULTS FOR BOUNDARY VALUE PROBLEMS FOR MULTIVALUED FRACTIONAL DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">34A60</style></keyword><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/03-dsa-35-50.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study the existence of solutions for a class of boundary value problems for fractional differential inclusions, where the right hand side is a convex or a non-convex multi-valued map. Suitable fixed point theorems are used to prove some new existence results. Examples illustrating the abstract results are also presented.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">35</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">C. Y. CHAN</style></author><author><style face="normal" font="default" size="100%">T. TREEYAPRASERT</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE, UNIQUENESS AND QUENCHING FOR A PARABOLIC PROBLEM WITH A MOVING NONLINEAR SOURCE ON A SEMI-INFINITE INTERVAL</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35B35</style></keyword><keyword><style  face="normal" font="default" size="100%">35K57</style></keyword><keyword><style  face="normal" font="default" size="100%">35K61</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/10-dsa-135-142.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let v and T be positive numbers, D = (0, ∞), Ω = D × (0, T ], and D¯ be the closure of D. This article studies the first initial-boundary value problem, ut − uxx = δ(x − vt)f (u(x, t)) in Ω, u(x, 0) = 0 on D, ¯ u(0, t) = 0, u(x, t) → 0 as x → ∞ for 0 &amp;lt; t ≤ T, where δ (x) is the Dirac delta function, and f is a given function such that limu→c− f(u) = ∞ for some positive constant c. It is shown that the problem has a unique nonnegative continuous solution u, and u(vt, t) is a strictly increasing function of t; also, if u exists for t ∈ [0, tq) with tq &amp;lt; ∞, then sup {u (x, t) : 0 ≤ x &amp;lt; ∞} reaches c − at tq.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">135</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">TADEUSZ JANKOWSKI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">FIRST-ORDER DIFFERENTIAL EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A40</style></keyword><keyword><style  face="normal" font="default" size="100%">34A45</style></keyword><keyword><style  face="normal" font="default" size="100%">34K10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/15-dsa-195-210.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study a first-order boundary value problem subject to some boundary conditions given by Riemann-Stieltjes integrals. Using a monotone iterative method, we formulate sufficient conditions which guarantee the existence of extremal or quasi-solutions in the corresponding region bounded by upper and lower solutions of our problems. The case when a unique solution exists is also investigated. Some examples are given to illustrate our results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">195</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MAREK MAJEWSKI</style></author><author><style face="normal" font="default" size="100%">STANISLAW WALCZAK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON A FRACTIONAL DIRICHLET PROBLEM OF HIGHER ORDER</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">34A08</style></keyword><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/38-DSA-479-490.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider a fractional version of some 2nth order Dirichlet problem. In the paper a sufficient condition for the existence of solution to the aforementioned problem is proved. The proved is based on some variational methods and application of a fractional counterpart of the du Bois-Reymond lemma for the order α ∈( n − 1/2 , n) (see [1])&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">479</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MUHAMMAD I. MUSTAFA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">GENERAL STABILITY IN MEMORY-TYPE THERMOELASTICITY WITH SECOND SOUND</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35B37</style></keyword><keyword><style  face="normal" font="default" size="100%">35L55</style></keyword><keyword><style  face="normal" font="default" size="100%">74D05</style></keyword><keyword><style  face="normal" font="default" size="100%">93D15</style></keyword><keyword><style  face="normal" font="default" size="100%">93D20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/26-DSA-327-340.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we consider an n-dimentional thermoelastic system of second sound with viscoelastic damping. We establish an explicit and general decay rate result without imposing restrictive assumptions on the behavior of the relaxation function at infinity. Our result allows a larger class of ralxation functions and generalizes previous results existing in the literature.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">327</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BOQUN OU</style></author><author><style face="normal" font="default" size="100%">BAOGUO JIA</style></author><author><style face="normal" font="default" size="100%">LYNN ERBE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A GENERALIZED HALANAY-TYPE INEQUALITY ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/31-DSA-389-398.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we obtain a Halanay-type inequality on time scales. By means of the obtained inequality, we get a new exponential stability condition for linear delay dynamic equations on time scales. An example is given to illustrate the results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">389</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">A S VATSALA</style></author><author><style face="normal" font="default" size="100%">M. SOWMYA</style></author><author><style face="normal" font="default" size="100%">D S  STUTSON</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">GENERALIZED MONOTONE METHOD FOR ORDINARY AND CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A08</style></keyword><keyword><style  face="normal" font="default" size="100%">34A12</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/34-DSA-429-438.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><section><style face="normal" font="default" size="100%">429</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Cemil Tunc</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">GLOBAL STABILITY AND BOUNDEDNESS OF SOLUTIONS TO DIFFERENTIAL EQUATIONS OF THIRD ORDER WITH MULTIPLE DELAYS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/37-DSA-467-478.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, the author gives certain sufficient conditions for the global asymptotic stability and boundedness of solutions to a class of functional differential equations of third order with multiple delays. The technique of proofs involve defining an appropriate Lyapunov– Krasovskii functional and applying LaSalle’s invariance principle. An example is discussed to illustrate the efficiency of the obtained results. Our results complement and improve some related ones in the literature.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">476</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">EBRU OZBILGE</style></author><author><style face="normal" font="default" size="100%">ALI DEMIR</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">IDENTIFICATION OF UNKNOWN COEFFICIENT IN TIME FRACTIONAL PARABOLIC EQUATION WITH MIXED BOUNDARY CONDITIONS VIA SEMIGROUP APPROACH</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35R11</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/27-DSA-341-348.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This article presents a semigroup approach for the mathematical analysis of the inverse coefficient problem of identifying the unknown coefficient k(x) in the linear time fractional parabolic equation D&lt;sup&gt;α&lt;/sup&gt;&lt;sub&gt;t&lt;/sub&gt; u(x, t) = (k(x)u&lt;sub&gt;x&lt;/sub&gt;)&lt;sub&gt;x&lt;/sub&gt;, 0 &amp;lt; α ≤ 1, with mixed boundary conditions u(0, t) = ψ&lt;sub&gt;0&lt;/sub&gt;(t), u&lt;sub&gt;x&lt;/sub&gt;(1, t) = ψ&lt;sub&gt;1&lt;/sub&gt;(t). Our aim is the investigation of the distinguishability of the input-output mapping Φ[·] : K → C[0, T ], via semigroup theory. This work shows that if the null space of the semigroup Tα,α(t) consists of only zero function, then the input-output mapping Φ[·] has distinguishability property. Also, the value k(0) of the unknown function k(x) is determined explicitly. In addition to these the boundary observation f(t) can be shown as an integral representation. This also implies that the mapping Φ[·] : K → C [0, T ] can be described in terms of the semigroup.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">341</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Martin J. Bohner</style></author><author><style face="normal" font="default" size="100%">RAMY R. MAHMOUD</style></author><author><style face="normal" font="default" size="100%">SAMIR H. SAKER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">IMPROVEMENTS OF DYNAMIC OPIAL-TYPE INEQUALITIES AND APPLICATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26D15</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A12</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/18-dsa-229-242.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we present some new improvements of dynamic Opial-type inequalities of first and higher order on time scales. We employ the new inequalities to prove several results related to the spacing between consecutive zeros of a solution and/or a zero of its derivative of a second-order dynamic equation with a damping term. The main results are proved by making use of a recently introduced new technique for Opial dynamic inequalities, the time scales integration by parts formula, the time scales chain rule, the time scales Taylor formula, and classical as well as time scales versions of H¨older’s inequality.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">229</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">TUNAHAN TURHAN</style></author><author><style face="normal" font="default" size="100%">NIHAT AYYILDIZ</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">INTEGRAL CURVES OF A LINEAR VECTOR FIELD IN SEMI-EUCLIDEAN SPACES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">53A04</style></keyword><keyword><style  face="normal" font="default" size="100%">53A35</style></keyword><keyword><style  face="normal" font="default" size="100%">53A40</style></keyword><keyword><style  face="normal" font="default" size="100%">53B30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/29-DSA-361-374.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we study integral curves or flow lines of a linear vector field in (2n+1)- dimensional semi-Euclidean space E&lt;sub&gt;ν&lt;/sub&gt;&lt;sup&gt;2n+1&lt;/sup&gt; . The skew symmetric matrix has been found depending on the number of timelike vectors are odd or even. Taking into consideration of the structure, we obtained the linear first order system of differential equations. This system gives rise to integral curves of linear vector fields. Meanwhile solution of the system has also been presented and discussed. Keywords. Integral curve, linear vector field, semi-Euclidean space, skew-symmetric matrix.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">361</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RAVI P. AGARWAL</style></author><author><style face="normal" font="default" size="100%">ABDULLAH OZBEKLER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">LYAPUNOV TYPE INEQUALITIES FOR SECOND ORDER SUB AND SUPER-HALF-LINEAR DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">34C15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/16-dsa-211-220.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In the case of oscillatory potential, we present a Lyapunov type inequality for second order differential equations of the form (r(t)Φβ(x ′ (t)))′ + q(t)Φγ(x(t)) = 0, in the sub-half-linear (0 &amp;lt; γ &amp;lt; β) and the super-half-linear (0 &amp;lt; β &amp;lt; γ &amp;lt; 2β) cases where Φ∗(s) = |s| ∗−1 s.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">211</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MÖNCH TYPE RESULTS FOR MAPS WITH WEAKLY ¨ SEQUENTIALLY CLOSED GRAPHS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H04</style></keyword><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/09-dsa-129-134.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">6</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we present fixed point results of Mönch type and a homotopy result for maps with weakly sequentially closed graphs.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">129</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">FULYA  DEREN</style></author><author><style face="normal" font="default" size="100%">NUKET  HAMAL</style></author><author><style face="normal" font="default" size="100%">TUGBA  CERDIK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MONOTONE ITERATIVE TECHNIQUE AND EXISTENCE RESULTS FOR FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10; 34B18; 34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">34K37</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/30-DSA-375-388.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper is concerned with the existence of positive solutions for boundary value problems of fractional functional differential equations involving the Caputo fractional derivative. The proof is based on the monotone iterative technique. As an application, an example is worked out to demonstrate the main result.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">375</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">YI LIU</style></author><author><style face="normal" font="default" size="100%">XIAOPING XUE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE MOTSCH-TADMOR MODEL WITH MULTIPLICATIVE WHITE NOISES IN FLOCKS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/40-DSA-503-522.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We enlarge the range of critical exponent β of the communication rate for unconditional flocking in the model proposed by Motsch, S. and Tadmor, E. [J. Statist. Phys., 141 (2011), 923–947], and describe an asymmetric stochastic model which emphasizes the asymmetric interaction between agents and employs the multiplicative white noise for the stochastic forces acting on ith-agent. For the case of asymmetric communication rate, we present sufficient conditions to guarantee the strong stochastic flocking to occur and show the almost sure exponential convergence toward constant equilibrium state through the control of the parameters and initial data. Our results are illustrated through the numerical simulations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">503</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MAREK T. MALINOWSKI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE NARROWING SET-VALUED STOCHASTIC INTEGRAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26E25</style></keyword><keyword><style  face="normal" font="default" size="100%">28B20</style></keyword><keyword><style  face="normal" font="default" size="100%">60G20</style></keyword><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword><keyword><style  face="normal" font="default" size="100%">93C41</style></keyword><keyword><style  face="normal" font="default" size="100%">93E03</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/32-DSA-399-418.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We analyze set-valued stochastic integral equations whose solutions are mappings with values in the hyperspace of subsets of square integrable random vectors space. In this paper we give a new formulation of these equations resulting in a new property of solutions. Namely, the diameter of the solution values will be a nonincreasing function. Hence we call these equations “narrowing”. We prove a result on existence and uniqueness of the solution to the narrowing setvalued stochastic integral equations. We establish a boundedness type result for the solution and an error of an approximate solution. Also the continuous dependence of the solution with respect to data of the equation is shown.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">399</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">CHARKAZ AGHAYEVA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NECESSARY CONDITIONS OF OPTIMALITY FOR STOCHASTIC SWITCHING CONTROL SYSTEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">49K45</style></keyword><keyword><style  face="normal" font="default" size="100%">93E20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/19-DSA-243-258.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper is devoted to optimal control problem of stochastic switching systems. Dynamics of this processes governed by stochastic differential equations with control terms in the drift and diffusion coefficients. Necessary conditions for optimality of described systems with the restrictions in each interval are obtained. The constraints on the transitions are described by the set of functional inclusions. Ekeland’s variational principle are applied to prove maximum principle in general form.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">243</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DAVID NIKOLAI CHEBAN</style></author><author><style face="normal" font="default" size="100%">CRISTIANA MAMMANA</style></author><author><style face="normal" font="default" size="100%">ELISABETTA MICHETTI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NON-AUTONOMOUS DIFFERENCE EQUATIONS: GLOBAL ATTRACTOR IN A BUSINESS-CYCLE MODEL WITH ENDOGENOUS POPULATION GROWTH</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">37B55</style></keyword><keyword><style  face="normal" font="default" size="100%">37C55</style></keyword><keyword><style  face="normal" font="default" size="100%">37C75</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/02-dsa-17-34.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;The article is devoted to the study of global attractors of quasi-linear non-autonomous difference equations and their structure. The results obtained are applied to the study of a twodimensional triangular economic growth model of Solow type with Variable Elasticity of Substitution production function and endogenous population growth rate described by the Beverton-Holt equation.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">17</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">NUKET AYKUT HAMAL</style></author><author><style face="normal" font="default" size="100%">FULYA YORUK DEREN</style></author><author><style face="normal" font="default" size="100%">TUGBA SENLIK CERDIK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NONLINEAR BOUNDARY VALUE PROBLEMS FOR p-LAPLACIAN FRACTIONAL DIFFERENTIAL SYSTEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/21-DSA-271-282.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we study the existence results of positive solutions for p-Laplacian fractional differential systems by means of fixed point theorems on cones. As an application, an example is given to demonstrate our main results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">271</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SYLWIA DUDEK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NONTRIVAL SOLUTION FOR NONLINEAR p(x)-LAPLACIAN DIRICHLET PROBLEM WITH THE SIGN-CHANGING WEIGHT</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/05-dsa-67-82.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we study the nonlinear elliptic problem involving p(x)-Laplacian with nonsmooth potential, where the weighted function λ may change sign. By using critical point theory for locally Lipschitz functionals due to Chang [6], we obtain conditions which ensure the existence of a solution for our problem.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">67</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">XUPING ZHANG</style></author><author><style face="normal" font="default" size="100%">PENGYU CHEN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NONTRIVIAL SOLUTIONS FOR NEUMANN BOUNDARY VALUE PROBLEM OF SECOND ORDER IMPULSIVE INTEGRO-DIFFERENTIAL EQUATIONS IN ORDERED BANACH SPACES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A37</style></keyword><keyword><style  face="normal" font="default" size="100%">34G20</style></keyword><keyword><style  face="normal" font="default" size="100%">34K30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/35-DSA-439-450.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper is devoted to study the existence of nontrivial solutions for second order Neumann boundary value problem with impulse effects in ordered Banach spaces. Under more general conditions of non-compactness measure and partial ordering, the existence of nontrivial solutions is obtained by employing the fixed point index theory of condensing mapping.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">349</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">NADEJDA E. DYAKEVICH</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON OCCURRENCE OF COMPLETE BLOW-UP OF THE SOLUTION FOR A DEGENERATE SEMILINEAR PARABOLIC PROBLEM WITH INSULATED BOUNDARY CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35K57</style></keyword><keyword><style  face="normal" font="default" size="100%">35K60</style></keyword><keyword><style  face="normal" font="default" size="100%">35K65</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/06-dsa-83-96.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let a, σ, p, q, r, and m be constants with a &amp;gt; 0, σ &amp;gt; 0, p ≥ 0, q ≥ 0, r &amp;gt; 1, and m &amp;gt; 0. This article studies the following degenerate semilinear parabolic initial-boundary value problem, ξ quτ − uξξ = ξ pu r for 0 &amp;lt; ξ &amp;lt; a, 0 &amp;lt; τ &amp;lt; σ, u(ξ, 0) = u0 (ξ) = m for 0 ≤ ξ ≤ a, uξ(0, τ) = 0 = uξ(a, τ) for τ &amp;gt; 0. We derive criteria for u to blow up in finite time, and estimate the blow-up rate. We show that the blow-up is regional if q &amp;gt; p; the blow-up is complete if q = p; and the blow-up cannot be complete if p &amp;gt; q.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">83</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ZHANG JINGXIAO</style></author><author><style face="normal" font="default" size="100%">CAO KAI</style></author><author><style face="normal" font="default" size="100%">D. KANNAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT IN JUMP DIFFUSION MARKETS WITH NO SHORT-SELLING AND NO BORROWING</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/13-dsa-169-186.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The optimal reinsurance and investment problem for insurance has attracted a lot of attention of researchers in the field of stochastic control for a long time. Along this line we discuss this problem in the case of jump diffusion markets when neither short-selling nor borrowing is allowed. Here, we specifically assume that the risk process of the insurance company is a diffusion process. The insurance company can transfer its risk by reinsurance and also invest its surplus in the financial market, where we model the price of the risky asset by a geometric L´evy process. To maximize the CARA (Constant Absolute Risk Aversion) utility of terminal wealth, the HJB equation with no short-selling constraint has been considered, and we obtain the closed form of the value function by a standard method. However, only a handful of people have discussed this problem under both constraints, (i.e. no short-selling and no borrowing). This is because the problem is much more general in this context, and becomes so complex that analytical solution could hardly be obtained. Therefore, we provide, under the no short-selling and no borrowing constraints, a numerical solution via Markov chain approximation, which proves to be effective and amenable.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">169</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">LESZEK GASINSKI</style></author><author><style face="normal" font="default" size="100%">NIKOLAOS  PAPAGEORGIOU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">PARAMETRIC p-LAPLACIAN EQUATIONS WITH SUPERLINEAR REACTIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35J20</style></keyword><keyword><style  face="normal" font="default" size="100%">35J60</style></keyword><keyword><style  face="normal" font="default" size="100%">35J92</style></keyword><keyword><style  face="normal" font="default" size="100%">58E05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/41-DSA-523-558.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">36</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider a parametric nonlinear Dirichlet problem driven by the p-Laplacian and with a Carath´eodory reaction which is (p − 1)-superlinear near ±∞ (but without satisfying the Ambrosetti-Rabinowitz condition) and (p − 1)-sublinear near zero. We show that for all values of the parameter λ &amp;gt; 0, the problem has at least three nontrivial solutions (two of constant sign). If we alter the geometry near the origin by introducing a “concave” nonlinearity (problem with combined nonlinearities), we show the existence of at least five nontrivial solutions (four of constant sign and the fifth nodal), when the parameter λ &amp;gt; 0 is small. Also, we produce extremal constant sign solutions u&lt;sup&gt;∗&lt;/sup&gt;&lt;sub&gt;λ&lt;/sub&gt; ∈ -int C&lt;sub&gt;+&lt;/sub&gt; and v&lt;sup&gt;∗&lt;/sup&gt;&lt;sub&gt;λ&lt;/sub&gt; ∈ −int C+. We investigate the monotonicity and continuity properties of the map λ→ u&lt;sup&gt;∗&lt;/sup&gt;&lt;sub&gt;λ&lt;/sub&gt; .&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">523</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ILKAY YASLAN KARACA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON POSITIVE SOLUTIONS FOR FOURTH-ORDER FOUR-POINT BOUNDARY VALUE PROBLEMS WITH ALTERNATING COEFFICIENT ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/25-DSA-313-326.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, by using four functionals fixed point theorem and five functionals fixed point theorem, we study the existence of at least one positive solution and three positive solutions respectively of a fourth-order four-point boundary value problem with alternating coefficient on a time scale. Examples are also included to illustrate our results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">313</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">HÜSEYIN TUNA</style></author><author><style face="normal" font="default" size="100%">AYTEKIN ERYILMAZ</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON q-STURM LIOUVILLE OPERATORS WITH EIGENVALUE PARAMETER CONTAINED IN THE BOUNDARY CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34L10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A13</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/39-DSA-491-502.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we study dissipative q-Sturm-Liouville operators with eigenvalue parameter contained in the boundary conditions by using Krein’s theorem. We proved a theorem on completeness of the system of eigenvectors and associated vectors of the dissipative q-Sturm-Liouville operators.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">491</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ABDESSLAM BALIKI</style></author><author><style face="normal" font="default" size="100%">MOUFFAK BENCHOHRA</style></author><author><style face="normal" font="default" size="100%">JUAN J. NIETO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">QUALITATIVE ANALYSIS OF SECOND ORDER FUNCTIONAL EVOLUTION INCLUSIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/42-DSA-559-572.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we investigate the existence and attractivity of mild solutions on infinite intervals to second order semilinear evolution inclusion with infinite delay in a Banach space. The proofs of the main results are based on Bohnenblust-Karlin’s fixed point theorem and the theory of evolution system.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">559</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ZHIGANG ZHANG</style></author><author><style face="normal" font="default" size="100%">XINZHI LIU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">RAZUMIKHIN-TYPE STABILITY THEOREMS FOR IMPULSIVE DISCRETE SYSTEMS WITH TIME DELAY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/04-dsa-51-66.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper studies impulsive discrete systems with time delay. Several criteria on uniform stability and uniform asymptotic stability are established by utilizing the Razumikhin technique. Both linear and nonlinear impulsive discrete systems with time delay are investigated. These stability criteria show that impulses can be used to stabilize a unstable system. Some numerical examples are presented to illustrate the stability criteria.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">51</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. H. SAKER</style></author><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author><author><style face="normal" font="default" size="100%">RAVI. P.  AGARWAL</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOME NEW DYNAMIC INEQUALITIES ON DISCRETE TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A15</style></keyword><keyword><style  face="normal" font="default" size="100%">26D10</style></keyword><keyword><style  face="normal" font="default" size="100%">26D15</style></keyword><keyword><style  face="normal" font="default" size="100%">34A40. 34N05</style></keyword><keyword><style  face="normal" font="default" size="100%">39A13</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/08-dsa-113-128.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper we prove some new dynamic inequalities on discrete time scales. These new inequalities contain some generalizations of the discrete inequalities due to Hardy, Copson, Leindler and Walsh. The main results will be proved using a general algebraic inequality and Keller’s chain rule on time scales.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">213</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MEHMET GÜRDAL</style></author><author><style face="normal" font="default" size="100%">ULAS YAMANCI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STATISTICAL CONVERGENCE AND SOME QUESTIONS OF OPERATOR THEORY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47B10</style></keyword><keyword><style  face="normal" font="default" size="100%">47B35</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/24-DSA-305-312.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">7</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;We use the concepts of statistical convergence and Berezin symbols for solving of some problems of operator theory. Namely, we prove that under some conditions the weak statistical limit of compact operators is compact. We also use statistical convergence for the solving of similar problem for the sequence of operators from Schatten-Neuman class. Some related questions are also discussed.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">305</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">TADEUSZ JANKOWSKI</style></author><author><style face="normal" font="default" size="100%">ROBERT JANKOWSKI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SYSTEMS OF BOUNDARY VALUE PROBLEMS OF ADVANCED DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A40</style></keyword><keyword><style  face="normal" font="default" size="100%">34A45</style></keyword><keyword><style  face="normal" font="default" size="100%">34K10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/14-dsa-187-194.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper considers the existence of extremal solutions to systems of advanced differential equations with corresponding nonlinear boundary conditions. The monotone iterative method is applied to obtain the existence results. An example is provided for illustration.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">187</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. H. SAKER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">APPLICATIONS OF OPIAL AND WIRTINGER INEQUALITIES ON ZEROS OF THIRD ORDER DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">34K11</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/31-DSA-31-15-new.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, for a third order differential equation, we will establish some new inequalities of Lyapunov type. These inequalities give implicit lower bounds on the distance between zeros of a nontrivial solution and also lower bounds for the spacing between zeros of a solution and/or its derivatives. The main results will be proved by making use of the H¨older inequality and some generalizations of Opial and Wirtinger type inequalities. Some examples are considered to illustrate the main results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">479</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BENEDETTA LISENA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ASYMPTOTIC STABILITY IN DELAYED PERIODIC EQUATIONS BY AVERAGE CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/09-DSA-384.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A new criterion is proposed for the global asymptotic stability of the positive periodic solution to the following delay logistic equation u ′ (t) = u(t)[ r(t) − a(t)u(t) − b(t)u(t − τ)] with continuous and periodic coefficients. Such condition, given in average form, incorporates some known pointwise assumptions. The same strategy is applied to study the linear case.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">129</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ZHENHAI LIU</style></author><author><style face="normal" font="default" size="100%">JIANGFENG HAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">BOUNDARY VALUE PROBLEMS FOR SECOND ORDER IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34G25</style></keyword><keyword><style  face="normal" font="default" size="100%">39J35</style></keyword><keyword><style  face="normal" font="default" size="100%">45N05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/25-DSA-840.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper is concerned with the existence and approximation of solutions for second order impulsive functional differential equations with boundary value conditions. By establishing new comparison results and applying the monotone iterative technique, we obtain the sufficient conditions for the existence of extremal solutions.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">369</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">XINQUAN ZHAO</style></author><author><style face="normal" font="default" size="100%">XINZHI LIU</style></author><author><style face="normal" font="default" size="100%">ZHIGANG ZHANG</style></author><author><style face="normal" font="default" size="100%">XIAOXIN LIAO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">BOUNDEDNESS AND DISSIPATION FOR DISCRETE-TIME DYNAMIC SYSTEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/05-DSA-30-14.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper studies boundedness and dissipation of solutions of a class of discretetime dynamic systems. By the method of Lyapunov functions, some necessary and sufficient criteria on boundedness, equi-boundedness, uniform boundedness, and uniform dissipation are established. In addition, some sufficient criteria on dissipation, equi-dissipation and uniform dissipation are also obtained. Some examples are given to illustrate our results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">55</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">PATRICIO GONZÁLEZ</style></author><author><style face="normal" font="default" size="100%">MANUEL PINTO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">COMPONENT-WISE CONDITIONS FOR THE ASYMPTOTIC EQUIVALENCE FOR NONLINEAR DIFFERENTIAL SYSTEMS WITH MAXIMA</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A20</style></keyword><keyword><style  face="normal" font="default" size="100%">34A30</style></keyword><keyword><style  face="normal" font="default" size="100%">34A36</style></keyword><keyword><style  face="normal" font="default" size="100%">34C41</style></keyword><keyword><style  face="normal" font="default" size="100%">34D05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/29-DSA-30-04.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We obtain new sufficient component-wise conditions for the asymptotic equivalence between bounded solutions of linear and nonlinear systems of differential equations with maxima. A Lipschitz component-wise and a spectral condition allow us to obtain vectorial asymptotic formulae. Under a spectral dichotomy condition the equivalences take the form of a homeomorphism which is also extended to unbounded solutions. We also obtain a vectorial Levinson’s theorem with maximum about asymptotic integration.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">439</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ILKAY YASLAN KARACA</style></author><author><style face="normal" font="default" size="100%">FATMA TOKMAK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF THREE POSITIVE SOLUTIONS FOR M-POINT TIME SCALE BOUNDARY VALUE PROBLEMS ON INFINITE INTERVALS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/24-DSA-778.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, by using the Leggett-Williams fixed point theorem and Five Functionals fixed point theorem, we establish the existence of three positive solutions for m-point time scale boundary value problems on infinite intervals. As an application, we also give some examples to demonstrate our results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">355</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DONNA STUTSON</style></author><author><style face="normal" font="default" size="100%">A. S. VATSALA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">GENERALIZED MONOTONE METHOD FOR CAPUTO FRACTIONAL DIFFERENTIAL SYSTEMS VIA COUPLED LOWER AND UPPER SOLUTIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">34A08</style></keyword><keyword><style  face="normal" font="default" size="100%">34A445</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/32-DSA-31-19.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Monotone method combined with the method of upper and lower solutions yields monotone sequences which converge uniformly and monotonically to minimal and maximal solutions of the nonlinear systems, when the forcing function is quasi monotone nondecreasing. In this paper we develop genearalized monotone method for N system of Caputo fractional differential equations when the forcing function is the sum of an increasing and decreasing functions. In generalized monotone method we use coupled upper and lower solutions and the method yields two monotone sequences which converge uniformly and monotonically to coupled minimal and maximal solutions. This method is applicable to the Lotka-Volterra equation with Caputo fractional derivative of order q when 0 &amp;lt; q ≤ 1. This provides an opportunity to provide better results or improve on the existing results with integer derivatives. Finally, under uniqueness condition we obtain the unique solution of the Caputo fractional differential system.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">495</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BO DU</style></author><author><style face="normal" font="default" size="100%">XIAOJING WANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">GLOBAL ATTRACTOR FOR NEUTRAL PARTIAL FUNCTIONAL INTEGRODIFFERENTIAL EQUATIONS WITH FINITE DELAY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35B41</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/10-DSA-662.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This work is devoted to investigating the existence of global attractors for a class of neutral partial functional integrodifferential equation with delay. Using the classic theory about global attractors in infinite dimensional dynamical systems, we obtain some sufficient conditions for guaranteeing the existence of a global attractor.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">139</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">M. ANDRIC</style></author><author><style face="normal" font="default" size="100%">J. PEČARIĆ</style></author><author><style face="normal" font="default" size="100%">I. PERIĆ</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">IMPROVEMENTS OF COMPOSITION RULE FOR THE CANAVATI FRACTIONAL DERIVATIVES AND APPLICATIONS TO OPIAL-TYPE INEQUALITIES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">26D15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/26-DSA-871.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper gives improvements of a composition rule for the Canavati fractional derivatives and presents improvements and weighted versions of Opial-type inequalities involving the Canavati fractional derivatives.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">383</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">TAHER S. HASSAN</style></author><author><style face="normal" font="default" size="100%">QINGKAI KONG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">INTERVAL CRITERIA FOR FORCED OSCILLATION OF DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN, DAMPING, AND MIXED NONLINEARITIES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">34C15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/19-DSA-31-17.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider forced second order differential equation with p-Laplacian and damping in the form of (r(t)φα0 (x ′ ))′ + p(t)φα0 (x ′ ) +X N j=0 qj (t)φαj (x) = e(t), where φα (u) := |u| α sgn u, αj &amp;gt; 0, j = 0, 1, 2, . . . , N, and r, p, qj , e ∈ C ([0, ∞), R) with r (t) &amp;gt; 0 on [0, ∞). Interval oscillation criteria of the El-Sayed type and the Kong type are obtained. These criteria are further extended to equations with deviating arguments. Our work generalizes, unifies, and improves many existing results in the literature.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">279</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">M. BARTUSEK</style></author><author><style face="normal" font="default" size="100%">John R. Graef</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">LIMIT-POINT/LIMIT-CIRCLE PROBLEM FOR SUB-HALF-LINEAR SECOND ORDER DELAY DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B20</style></keyword><keyword><style  face="normal" font="default" size="100%">34C11</style></keyword><keyword><style  face="normal" font="default" size="100%">34C15</style></keyword><keyword><style  face="normal" font="default" size="100%">34D05</style></keyword><keyword><style  face="normal" font="default" size="100%">34K11</style></keyword><keyword><style  face="normal" font="default" size="100%">34K12</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/18-DSA-31-16.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The authors investigate the limit-point and limit-circle properties of solutions of the delay differential equation a(t)|y ′ | p−1 y ′ ′ + r(t)  y ϕ(t)   λ sgn y ϕ(t)  = 0 where p ≥ λ ≥ 1, a(t) &amp;gt; 0, r(t) &amp;gt; 0, ϕ(t) ≤ t on R+, and limt→∞ ϕ(t) = ∞. The results generalize these properties for ordinary (non-delay) differential equations that were initiated by Hermann Weyl one hundred years ago for linear equations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">261</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">J. D. RAM´IREZ</style></author><author><style face="normal" font="default" size="100%">A. S. VATSALA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MONOTONE METHOD FOR NONLINEAR CAPUTO FRACTIONAL BOUNDARY VALUE PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">34A08</style></keyword><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/06-DSA-30-15.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, by using upper and lower solutions, we develop monotone method for the nonlinear Caputo fractional boundary value problem of order α where 1 &amp;lt; α &amp;lt; 2. We construct two sequences which converge uniformly and monotonically to the extremal solutions of the nonlinear Caputo fractional boundary value problem.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">73</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">GABRIELE BONANNO</style></author><author><style face="normal" font="default" size="100%">SHAPOUR HEIDARKHANI</style></author><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MULTIPLE SOLUTIONS FOR A CLASS OF DIRICHLET QUASILINEAR ELLIPTIC SYSTEMS DRIVEN BY A (P, Q)-LAPLACIAN OPERATOR</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Critical point</style></keyword><keyword><style  face="normal" font="default" size="100%">Dirichlet Systems</style></keyword><keyword><style  face="normal" font="default" size="100%">Multiplicity results</style></keyword><keyword><style  face="normal" font="default" size="100%">Three solutions</style></keyword><keyword><style  face="normal" font="default" size="100%">Variational methods</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/07-DSA-31-03.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We investigate the existence of three distinct solutions for a class of Dirichlet quasilinear elliptic systems driven by a (p, q)-Laplacian operator. The technical approach is fully based on a very recent three critical points theorem.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">89</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BARUCH CAHLON</style></author><author><style face="normal" font="default" size="100%">DARRELL SCHMIDT</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NECESSARY CONDITIONS AND ALGORITHMIC STABILITY TESTS FOR CERTAIN HIGHER ODD ORDER NEUTRAL DELAY DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">asymptotic stability</style></keyword><keyword><style  face="normal" font="default" size="100%">characteristic functions</style></keyword><keyword><style  face="normal" font="default" size="100%">delay</style></keyword><keyword><style  face="normal" font="default" size="100%">necessary conditions</style></keyword><keyword><style  face="normal" font="default" size="100%">stability criteria</style></keyword><keyword><style  face="normal" font="default" size="100%">stability regions</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/16-DSA-31-12.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">23</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we obtain necessary conditions and robust algorithmic criteria for asymptotic stability of the zero solution of higher odd order linear neutral delay differential equations of the form y (2m+1)(t) + αy(2m+1)(t − τ) = X 2m j=0 ajy (j) (t) +X 2m j=0 bjy (j) (t − τ) where aj , bj, and α 6=&amp;nbsp;0 are real constants. Here τ &amp;gt; 0 is a constant delay. In proving our results we make use of Pontryagin’s theory for quasi-polynomials.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">223</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">TADEUSZ JANKOWSKI</style></author><author><style face="normal" font="default" size="100%">ROBERT JANKOWSKI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON NEUTRAL DIFFERENTIAL EQUATIONS AND THE MONOTONE ITERATIVE METHOD</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A12</style></keyword><keyword><style  face="normal" font="default" size="100%">34A45</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/22-DSA-633.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The application of the monotone iterative method to neutral differential equations with deviating arguments is considered in this paper. We formulate existence results giving suffi- cient conditions which guarantee that such problems have solutions. This approach is new and to the Authors’ knowledge, this is the first paper when the monotone iterative method is applied to neutral first–order differential equations with deviating arguments. An example is given to illustrate theoretical results. One may apply a numerical method based on the proposed monotone iterative method to obtain a numerical solution of our problems.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">317</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RUN XU</style></author><author><style face="normal" font="default" size="100%">RUN XU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NEW OSCILLATION CRITERIA FOR CERTAIN EVEN ORDER DELAY DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34D</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/20-DSA-364.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;For even order delay differential equation of the form [p(t)|x (n−1)(t)| α−1x (n−1)(t)]′ + F(t, x(g(t)) = 0, n even where p ∈ C 1 ([t0, ∞); (0, ∞)), F ∈ C([t0, ∞) × R; R), g ∈ C([t0, ∞); R), and α &amp;gt; 0 is a constant, we obtain several new oscillation criteria without assumptions that has been required for the related results obtained before, our results generalize and improve many known conclusions.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">295</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MOHAMED ABDALLA DARWISH</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NONDECREASING SOLUTIONS OF A FRACTIONAL QUADRATIC INTEGRAL EQUATION OF URYSOHN-VOLTERRA TYPE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">45G10</style></keyword><keyword><style  face="normal" font="default" size="100%">45M99</style></keyword><keyword><style  face="normal" font="default" size="100%">47H09</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/28-DSA-1175.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we study a very general quadratic integral equation of fractional order. We show that the quadratic integral equations of fractional orders has at least one monotonic solution in the Banach space of all real functions defined and continuous on a bounded and closed interval. The concept of a measure of noncompactness related to monotonicity, introduced by J. Bana´s and L. Olszowy, and a fixed point theorem due to Darbo are the main tools in carrying out our proof. In fact we generalize, improve the results of the paper [M.A. Darwish, On quadratic integral equation of fractional orders, J. Math. Anal. Appl. 311 (2005), 112–119]. Also, we extend and generalize the results of the paper [J. Bana´s and B. Rzepka, Monotonic solutions of a quadratic integral equation of fractional order, J. Math. Anal. Appl. 332 (2007), 1370–1378].&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">423</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DA_BIN WANG</style></author><author><style face="normal" font="default" size="100%">WEN GUAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NONLINEAR FIRST-ORDER SEMIPOSITONE PROBLEMS OF IMPULSIVE DYNAMIC EQUATIONS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/21-DSA-456.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;By using the well-known Guo-Krasnoselskii fixed point theorem, in this paper, some results of one positive solution to a class of nonlinear first-order semipositone problems of impulsive dynamic equations on time scales are obtained. One example is given to illustrate the main results in this paper.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">307</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ABDELKADER BOUCHERIF</style></author><author><style face="normal" font="default" size="100%">SOTIRIS K. NTOUYAS</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NONLOCAL INITIAL VALUE PROBLEMS FOR FIRST ORDER FRACTIONAL DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">34B05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/17-DSA-31-13.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we study the existence of solutions of initial value problems for first order fractional differential equations with nonlocal conditions. A variety of new existence results are presented which are based on known fixed point theorems. Our results extend previous results in integer and time scales cases to the fractional case.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">247</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">QINGSHAN YANG</style></author><author><style face="normal" font="default" size="100%">CHUNYAN JI</style></author><author><style face="normal" font="default" size="100%">DAQING JIANG</style></author><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author><author><style face="normal" font="default" size="100%">RAVI P. AGARWAL</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A NOTE ON A STOCHASTIC PERTURBED DI SIR EPIDEMIC MODEL</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Itˆo’s formula</style></keyword><keyword><style  face="normal" font="default" size="100%">Stochastic DI SIR epidemic model</style></keyword><keyword><style  face="normal" font="default" size="100%">Stochastic Lyapunov function</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/13-DSA-31-02.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we investigate the asymptotic behavior of a DI SIR epidemic model with a stochastic perturbation. The ergodic property is obtained by stochastic Lyapunov functions. We also make simulations to show how the solution goes around the endemic equilibrium of a deterministic system under conditions, which conform to our analytical result.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">183</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JINGXIAO ZHANG</style></author><author><style face="normal" font="default" size="100%">SHENG LIU</style></author><author><style face="normal" font="default" size="100%">D. KANNAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OPTIMAL DIVIDEND AND REINSURANCE UNDER THRESHOLD STRATEGY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword><keyword><style  face="normal" font="default" size="100%">60H30</style></keyword><keyword><style  face="normal" font="default" size="100%">93E20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/14-DSA-31-07.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider the optimal dividend and reinsurance problems in this article, where the dividend strategy is the threshold strategy and the reinsurance is the proportional reinsurance. Despite the fact that the barrier strategy has its popularity in theoretical research, such a strategy has little practical acceptance as it will lead to the certainty of ultimate ruin. A modified version of the barrier strategy is the threshold strategy which assumes that dividends are paid at a rate smaller than the rate of premium income whenever the surplus is above some threshold level, and that no dividends are paid out whenever the surplus is below the threshold level. In this article, we consider two cases of the threshold strategy. One is the threshold strategy without barrier, and the other is the threshold strategy with barrier. The first case generalizes and corrects part of results in [16]. In the second case, we use the stochastic control theoretic techniques, to find the value function as well as the optimal investment-reinsurance policy in closed form.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">193</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JINGXIAO ZHANG</style></author><author><style face="normal" font="default" size="100%">SHENG LIU</style></author><author><style face="normal" font="default" size="100%">D. KANNAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OPTIMAL DIVIDEND PROBLEM WITH THE INFLUENCE OF DIVIDEND PAYOUTS ON INSURANCE BUSINESS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword><keyword><style  face="normal" font="default" size="100%">60H30</style></keyword><keyword><style  face="normal" font="default" size="100%">93E20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/34-DSA-31-21.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This article initiates the optimal dividend problem, from the view point of the managers of the insurance companies. where we incorporate the influence of dividend payouts on the insurance business. We begin with a mathematical characterization of the influence of dividend payouts, and then continue to find the optimal dividend policy that maximizes the expected utility of terminal wealth and minimizes the ruin probability. We study the problem in terms of the Levy process and derive the diffusion process case as a particular one.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">519</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">N. U. AHMED</style></author><author><style face="normal" font="default" size="100%">M. SURUZ MIAH</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OPTIMAL FEEDBACK CONTROL LAW FOR A CLASS OF PARTIALLY OBSERVED UNCERTAIN DYNAMIC SYSTEMS: A MIN-MAX PROBLEM</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Differential Inclusion</style></keyword><keyword><style  face="normal" font="default" size="100%">Necessary Conditions of Optimality</style></keyword><keyword><style  face="normal" font="default" size="100%">Optimal Feedback Control Law</style></keyword><keyword><style  face="normal" font="default" size="100%">Uncertain Nonlinear Dynamic systems</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/11-DSA-31-01.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">19</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we consider a class of partially observed dynamic systems with measurement uncertainty and present a technique for design of optimal linear output feedback controls to minimize the maximum risk. This is then extended to cover systems with uncertainty in the measurement as well as in the dynamics. These results are presented in the form of necessary conditions of optimality. Theoretical results are illustrated by numerical examples.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">149</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JINGXIAO ZHANG</style></author><author><style face="normal" font="default" size="100%">SHENG LIU</style></author><author><style face="normal" font="default" size="100%">D. KANNAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OPTIMAL INVESTMENT AND PROPORTIONAL REINSURANCE UNDER NO SHORT-SELLING AND NO BORROWING</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword><keyword><style  face="normal" font="default" size="100%">60H30</style></keyword><keyword><style  face="normal" font="default" size="100%">93E20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/15-DSA-31-10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Insurance companies resort to investment and reinsurance, among other options, to manage their reseerves. This article addresses the problem of optimal investment and reinsurance when no short-selling and no borrowing allowed. More specifically, we assume that the risk process of the insurance company is a compound Poisson process perturbed by a standard Brownian motion and that the risk can be reduced through a proportional reinsurance. In addition, the surplus can be invested in the financial market such that the portfolio will consist, for simplicity, of one risky asset and one risk-free asset. Our goal is to find the optimal investment and reinsurance policy which can maximize the expected exponential utility of the terminal wealth. In the case of no short-selling, we find the closed form of value function as well as the optimal investment-reinsurance policy. In the case when neither short-selling nor borrowing allowed, the resulting HJB equation is difficult to solve analytically, and hence we provide a numerical solution through Markov chain approximation techniques&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">205</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SAID R. GRACE</style></author><author><style face="normal" font="default" size="100%">RAVI P. AGARWAL</style></author><author><style face="normal" font="default" size="100%">SANDRA PINELAS</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE OSCILLATION OF FOURTH ORDER SUPERLINEAR DYNAMIC EQUATIONS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/04-DSA-30-12.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Some oscillation criteria for the oscillatory behavior of fourth order superlinear dynamic equations on time scales are established. Criteria are proved that ensure that all solutions of superlinear and linear equations are oscillatory. Many of our results are new for corresponding fourth order superlinear differential equations and fourth order superlinear difference equations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">45</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MUJEEB UR REHMAN</style></author><author><style face="normal" font="default" size="100%">RAHMAT ALI KHAN</style></author><author><style face="normal" font="default" size="100%">PAUL  W. ELOE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">POSITIVE SOLUTIONS OF NONLOCAL BOUNDARY VALUE PROBLEM FOR HIGHER ORDER FRACTIONAL DIFFERENTIAL SYSTEM</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/12-DSA-30-11.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we study existence and multiplicity results for a coupled system of nonlinear nonlocal boundary value problems for higher order fractional differential equations of the type    cDα 0+u(t) = λa(t)f(u(t), v(t)), cD β 0+v(t) = µb(t)g(u(t), v(t)), u ′ (0) = u ′′(0) = u ′′′(0) = · · · = u (n−1)(0) = 0, u(1) = ξ1u(η1), v ′ (0) = v ′′(0) = v ′′′(0) = · · · = v (n−1)(0) = 0, v(1) = ξ2v(η2), where λ, µ &amp;gt; 0, n − 1 &amp;lt; α, β ≤ n for n ∈ N; ξi , ηi ∈ (0, 1) for i = 1, 2 and cDα 0+ is Caputo fractional derivative. We employ the Guo-Krasnosel’skii fixed point theorem to establish existence and multiplicity results for positive solutions. We derive explicit intervals for the parameters λ and µ for which the system possess the positive solutions or multiple positive solutions. Examples are included to show the applicability of the main results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">169</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">TADEUSZ JANKOWSKI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">POSITIVE SOLUTIONS TO THIRD-ORDER IMPULSIVE STURM-LIOUVILLE BOUNDARY VALUE PROBLEMS WITH DEVIATED ARGUMENTS AND ONE-DIMENSIONAL p-LAPLACIAN</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/39-DSA-31-09.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we establish the existence of at least three positive solutions for thirdorder impulsive Sturm-Liouville boundary value problems with p-Laplacian, by a fixed point theorem due to Avery and Peterson. We discuss our problem both for advanced and delayed arguments. An example is included to illustrate that corresponding assumptions are satisfied. Key words: Differential equations with advanced and delayed arguments, p-Laplacian, multiple positive solutions, the fixed point theorem due to Avery and Peterson&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">575</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">HONG-BO SHI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">QUALITATIVE ANALYSIS OF A DIFFUSIVE PREDATOR-PREY MODEL WITH BEDDINGTON-DEANGELIS FUNCTIONAL RESPONSE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35J60; 35K55; 92D25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/01-DSA-268.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper is concerned with a diffusive predator-prey model with BeddingtonDeAngelis functional response under Robin boundary conditions. We establish the existence and nonexistence of coexistence solutions and give some sufficient and necessary conditions. In addition, the stability of coexistence solutions is investigated. Furthermore, the extinction and permanence of time-dependent system are discussed.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">1</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">C. Y. CHAN</style></author><author><style face="normal" font="default" size="100%">P. TRAGOONSIRISAK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A QUENCHING PROBLEM DUE TO A CONCENTRATED NONLINEAR SOURCE IN AN INFINITE STRIP</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35B35</style></keyword><keyword><style  face="normal" font="default" size="100%">35K55</style></keyword><keyword><style  face="normal" font="default" size="100%">35K57</style></keyword><keyword><style  face="normal" font="default" size="100%">35K60</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/33-DSA-31-20.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This article studies a semilinear parabolic initial-boundary value problem with a concentrated nonlinear source in an infinite strip in the N-dimensional Euclidean space. Existence, uniqueness, and locations where quenching occurs for the solution are investigated.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">505</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">GEORGE A. ANASTASSIOU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">RIGHT DELTA DISCRETE FRACTIONALITY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">26D15</style></keyword><keyword><style  face="normal" font="default" size="100%">26D20</style></keyword><keyword><style  face="normal" font="default" size="100%">34A25</style></keyword><keyword><style  face="normal" font="default" size="100%">39A12</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/35-DSA-31-22.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Here we define a Caputo like right discrete delta fractional difference and we produce a right discrete delta fractional Taylor formula for the first time. We estimate the remainder. Then we produce related right discrete delta fractional Ostrowski, Poincar´e and Sobolev type inequalities.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">531</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">P. KARTHIKEYAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOME RESULTS FOR BOUNDARY VALUE PROBLEM OF AN INTEGRO DIFFERENTIAL EQUATIONS WITH FRACTIONAL ORDER</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K05;26A33</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/02-DSA-291.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper discusses boundary value problem for fractional integrodifferential equations. We establish existence results by using the applications of Krasnoselkii theorem. An example is discussed to illustrate the efficiency of the obtained results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">17</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ALEXANDER J. ZASLAVSKI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STABILITY OF A TURNPIKE PHENOMENON FOR THE ROBINSON-SOLOW-SRINIVASAN MODEL</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">49J99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/03-DSA-30-10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study the structure of solutions for a class of discrete-time optimal control problems. These control problems arise in economic dynamics and describe a model proposed by Robinson, Solow and Srinivasan. We are interested in turnpike properties of the approximate solutions which are independent of the length of the interval, for all sufficiently large intervals. In the present paper we show that these turnpike properties are stable under perturbations of an objective function.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">25</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BELKACEM SAID-HOUARI</style></author><author><style face="normal" font="default" size="100%">RADOUANE RAHALI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A STABILITY RESULT FOR A TIMOSHENKO SYSTEM WITH PAST HISTORY AND A DELAY TERM IN THE INTERNAL FEEDBACK</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35B37</style></keyword><keyword><style  face="normal" font="default" size="100%">35L55</style></keyword><keyword><style  face="normal" font="default" size="100%">74D05</style></keyword><keyword><style  face="normal" font="default" size="100%">93D15</style></keyword><keyword><style  face="normal" font="default" size="100%">93D20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/23-DSA-754.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">27</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we consider a Timoshenko system with a delay term in the feedback and memory term. Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove a well posedness result. Furthermore an exponential stability result has been shown if the weight of the damping is greater or equal to the weight of the delay. We distinguish two cases: the case where the weight of the delay is less than the weight of the damping and the case where the two weights are equal. In each case we introduce an appropriate Lyapunov functional which leads to an exponential stability. This result extends the one in [15] and the recent result in [23].&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">327</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BAPURAO C. DHAGE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THEORETICAL APPROXIMATION METHODS FOR HYBRID DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/30-DSA-31-08.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">23</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, some existence theorems for the extremal solutions are proved for an initial value problem of nonlinear hybrid differential equations via constructive methods. The monotone iterative techniques for initial value problems of first order hybrid differential equations are developed and it is shown that the sequences of successive iterations defined in a certain way converge to the minimal and maximal solutions of the hybrid differential equations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">455</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SHAPOUR HEIDARKHANI</style></author><author><style face="normal" font="default" size="100%">YU TIAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THREE SOLUTIONS FOR A CLASS OF GRADIENT KIRCHHOFF-TYPE SYSTEMS DEPENDING ON TWO PARAMETERS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">47J10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/37-DSA-517.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we shall discuss the existence of at least three solutions for the class of two-point boundary value Kirchhoff-type systems&lt;/p&gt;

&lt;p&gt;( −Ki( Rb a |u ′ i (x)| 2dx)u ′′ i = λFui (x, u1, . . . , un) + µGui (x, u1, . . . , un), ui(a) = ui(b) = 0&lt;/p&gt;

&lt;p&gt;for 1 ≤ i ≤ n. The approach is fully based on a recent three critical points theorem of B. Ricceri [A three critical points theorem revisited, Nonlinear Anal. 70/9 (2009) 3084–3089]&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">551</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">TOPOLOGICAL PRINCIPLES FOR ESSENTIAL TYPE MAPS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword><keyword><style  face="normal" font="default" size="100%">47H11</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/36-DSA-31-23.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we present a definition of d-essential and d-L-essential maps in a very general setting and we establish a homotopy property for both d-essential and d-L-essential maps.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">541</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ALEXANDER J. ZASLAVSKI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A TURNPIKE PROPERTY OF APPROXIMATE SOLUTIONS OF AN OPTIMAL CONTROL PROBLEM ARISING IN ECONOMIC DYNAMICS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">49J99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/27-DSA-30-18.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">27</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study the structure of approximate solutions for a class of continuous-time optimal control problems. These optimal control problems arise in economic dynamics and describe a model proposed by Robinson, Solow and Srinivasan. We are interested in turnpike properties of the approximate solutions which are independent of the length of the interval, for all sufficiently large intervals.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">395</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">R. H. LIU</style></author><author><style face="normal" font="default" size="100%">Q. ZHANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">VALUATION OF GUARANTEED EQUITY-LINKED LIFE INSURANCE UNDER REGIME-SWITCHING MODELS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">93E03</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/08-DSA-352.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">27</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper is concerned with the valuation of guaranteed equity-linked life insurance. The underlying reference equity fund and interest rate are dictated by a set of diffusions coupled by a finite state Markov chain. Two approaches are developed for pricing European options that are embedded in the life insurance contracts. The first approach involves a discounted characteristic function and inversion of Fourier transform. The second approach follows a Monte-Carlo simulation technique. These two approaches together with a bond valuation procedure are used to determine the fair value of the guaranteed equity-linked life insurance contracts. Finally, numerical examples are provided to illustrate the results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">101</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">FANWEI MENG</style></author><author><style face="normal" font="default" size="100%">LIANZHONG LI</style></author><author><style face="normal" font="default" size="100%">YUZHEN BAI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Ψ-STABILITY OF NONLINEAR VOLTERRA INTEGRO-DIFFERENTIAL SYSTEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">45J05</style></keyword><keyword><style  face="normal" font="default" size="100%">45M10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/38-DSA-523.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we give some sufficient conditions for Ψ-(uniform) stability of the trivial solution of the nonlinear differential systems and of a nonlinear Volterra integro-differential system.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">563</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SAMUEL CASTILLO</style></author><author><style face="normal" font="default" size="100%">MANUEL PINTO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ASYMPTOTIC BEHAVIOR OF FUNCTIONAL DYNAMIC EQUATIONS IN TIME SCALE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/12-DSA-229.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;It is considered a scalar linear functional dynamic equation in time scale with delayed argument of the form&lt;/p&gt;

&lt;p&gt;(0.1)&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;y&lt;sup&gt;∆&lt;/sup&gt;(t) = b(t) y( τ(t) ), t ∈ T ∩ [0, +∞]&lt;/p&gt;

&lt;p&gt;where T, the time scale, is a closed subset of R without upper bound for this case,&lt;sup&gt; ∆&lt;/sup&gt; is de Hilger’s derivate, which among other things, unifies difference operator for sequences and the derivate. The functions b, τ : T → C, τ &amp;gt; 0, are “locally integrable” and satisfy integral smallness conditions in a sense to be defined later. Asymptotic formulas of solutions of equation (0.1) are given. They unify and extend asymptotic formulas of difference and differential equations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">165</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">P. T. NAM</style></author><author><style face="normal" font="default" size="100%">H. M. HIEN</style></author><author><style face="normal" font="default" size="100%">V. N. PHAT</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ASYMPTOTIC STABILITY OF LINEAR STATE-DELAYED NEUTRAL SYSTEMS WITH POLYTOPE TYPE UNCERTAINTIES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34D20</style></keyword><keyword><style  face="normal" font="default" size="100%">37C75</style></keyword><keyword><style  face="normal" font="default" size="100%">93D20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/05-DSA-05.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, a class of linear state-delayed neutral systems with polytope type uncertainties is studied. Using an improved Lyapunov Krasovskii parameter-dependent functional and linear matrix inequality (LMI) technology, new delay-dependent sufficient conditions for the asymptotic stability of the system are first established in terms of Mondie-Kharitonov type’s LMI conditions.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">63</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RUYUN MA</style></author><author><style face="normal" font="default" size="100%">JIA XU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">BIFURCATION FROM INTERVAL AND POSITIVE SOLUTIONS FOR SECOND ORDER PERIODIC BOUNDARY VALUE PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">34G20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/16-DSA-240.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We give a global description of the branches of positive solutions of second order periodic boundary value problems&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; u′′− q(t)u + λa(t) f(u)= 0,&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;0 &amp;lt; t &amp;lt; 2π,&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;u(0) = u(2π),&amp;nbsp; &amp;nbsp;u′(0) = u′(2π)&lt;/p&gt;

&lt;p&gt;which are not necessarily linearizable. Our approach based on topological degree and global bifurcation techniques.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">211</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JONG-SHENQ GUO</style></author><author><style face="normal" font="default" size="100%">CHANG-SHOU LIN</style></author><author><style face="normal" font="default" size="100%">MASAHIKO SHIMOJO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">BLOW-UP BEHAVIOR FOR A PARABOLIC EQUATION WITH SPATIALLY DEPENDENT COEFFICIENT</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/30-DSA-30-03.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">19</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study the initial boundary value problem and Cauchy problem for the semilinear heat equation with power nonlinearity and spatially dependent coefficient. First, for the initial boundary value problem, we establish several conditions that ensure the origin is not a blow-up point. Then the Cauchy problem for a special case is also studied. Finally, we derive the blow-up rate when the origin is not a blow-up point.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">415</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">TADEUSZ JANKOWSKI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">BOUNDARY VALUE PROBLEMS FOR DYNAMIC EQUATIONS WITH ADVANCED ARGUMENTS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A10</style></keyword><keyword><style  face="normal" font="default" size="100%">34A45</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/42-DSA-300.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper considers boundary value problems on time scales and also discusses inequalities on time scales. We formulate sufficient conditions under which such problems have extremal solutions in a corresponding region bounded by upper and lower solutions. Examples are also included to illustrate the importance of the result obtained.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">599</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">TADEUSZ JANKOWSKI</style></author><author><style face="normal" font="default" size="100%">ROBERT JANKOWSKI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">BOUNDARY VALUE PROBLEMS WITH ADVANCED ARGUMENTS INVOLVING UPPER AND LOWER SOLUTIONS IN REVERSE ORDER</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A10</style></keyword><keyword><style  face="normal" font="default" size="100%">34A45</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/40-DSA-295.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we discuss boundary value problems for first order differential-integral equations with advanced arguments. We formulate sufficient conditions, under which such problems have a minimal and a maximal solution in a corresponding region bounded by upper-lower solutions. To get our results we apply a new approach based on Heikkila and V.Lakshmikantham theorem [1]. An example illustrates the results obtained.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">577</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SMAIL DJEBALI</style></author><author><style face="normal" font="default" size="100%">SAMIRA ZAHAR</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">BOUNDED SOLUTIONS FOR A DERIVATIVE DEPENDENT BOUNDARY VALUE PROBLEM ON THE HALF-LINE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">34B40</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/38-DSA-266.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper is devoted to the existence of bounded solutions to a nonlinear secondorder boundary value problem on the positive half-line where the nonlinearity depends on the first derivative. We employ topological degree theory combined with the method of upper and lower solutions on compact domains to prove existence of solution on truncated domains. Solutions are then extended to unbounded domains using sequential arguments. A uniqueness result is also obtained and two illustrative examples end the paper.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">545</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MEIRONG ZHANG</style></author><author><style face="normal" font="default" size="100%">ZHE ZHOU</style></author><author><style face="normal" font="default" size="100%">MING LI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">CLASSIFICATION OF SOLUTIONS OF ASYMMETRIC p-LAPLACIAN OSCILLATORS WITH PERIODIC COEFFICIENTS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34D08</style></keyword><keyword><style  face="normal" font="default" size="100%">37A25</style></keyword><keyword><style  face="normal" font="default" size="100%">37E10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/11-DSA-225.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;By exploiting the Denjoy theorem in topological dynamics and the unique ergodic theorem in ergodic theory, we will give a classification of all solutions of asymmetric p-Laplacian oscillators with periodic coefficients.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">147</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">H. ADIBI</style></author><author><style face="normal" font="default" size="100%">XINZHI LIU</style></author><author><style face="normal" font="default" size="100%">M. SHOJAEI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">CONVERGENCE CRITERIA FOR A CLASS OF SECOND-ORDER DIFFERENCE EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/06-DSA-06.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper studies a class of nonlinear second order difference equations of the type x&lt;sub&gt;n+1&lt;/sub&gt; = f(x&lt;sub&gt;n&lt;/sub&gt;, x&lt;sub&gt;n−1&lt;/sub&gt;) / x&lt;sub&gt;n&lt;/sub&gt; , where f is symmetric and monotonic with initial conditions x−1, x0 being positive real numbers. Some sufficient conditions under which every positive solution of such equation converges to a period two solution or to the cycle {0, ∞} are established.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">73</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">GUOLIANG WANG</style></author><author><style face="normal" font="default" size="100%">QINGLING ZHANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">DELAY-DEPENDENTH∞ CONTROL FOR MARKOVIAN JUMP SYSTEMS WITH DELAYS VARYING IN A RANGE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/43-DSA-312.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper presents a new method for H&lt;sub&gt;∞&lt;/sub&gt; state feedback controller design of Markovian jump systems with delays varying in a range. Firstly, results on delay-dependent stability and H&lt;sub&gt;∞&lt;/sub&gt; performance are established by exploiting a new Lyapunov functional making full use of information about time delay and Jensen’s inequality. Neither free weighting variables nor model transformation is used in the derivation of less conservative criteria. Secondly, based on the obtained conditions, a new design of state feedback controller is developed in terms of linear matrix inequalities (LMIs). Finally, illustrative examples are presented to show the advantage and validity of the proposed approaches.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">611</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">C. RATTANAKUL</style></author><author><style face="normal" font="default" size="100%">Y. LENBURY</style></author><author><style face="normal" font="default" size="100%">J. KONGSON</style></author><author><style face="normal" font="default" size="100%">W. TRIAMPO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE DYNAMICS OF A NONLINEAR MODEL OF SIGNAL TRANSDUCTION IN HUMAN UNDER IMPULSIVE DEPRESSANT DRUG TREATMENT</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/46-DSA-30-06.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A mathematical model of the signal transduction process, involving hormone coupled receptors and an inhibiting enzyme, under impulsive depressant treatment, is proposed and analyzed. We show that there is a stable periodic solution, at the vanishing density of the ligand bound receptors on the cell membrane and plasmalemma, when the impulsive period is less than some critical value. The conditions for permanence of the system are then given. Finally, it is shown that as the impulsive period increases beyond a certain critical value, the emergence of stable positive periodic solution may be observed under appropriate conditions on the system parameters.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">651</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ROGER D. KIRBY</style></author><author><style face="normal" font="default" size="100%">A. G. LADDE</style></author><author><style face="normal" font="default" size="100%">G. S. LADDE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ENERGY FUNCTION METHOD FOR SOLVING NONLINEAR DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/24-DSA-29-09.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A very general conceptual algorithm for finding a solution process of a first order nonlinear differential equation is presented. The scope of this method is exhibited by showing the existing methods of solving nonlinear differential equations as special cases. Moreover, this approach extends for solving a larger class of nonlinear differential equations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">335</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DA-BIN WANG</style></author><author><style face="normal" font="default" size="100%">XIA-YI WANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF POSITIVE SOLUTIONS FOR NONLINEAR FIRST-ORDER IMPULSIVE DYNAMIC EQUATIONS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/35-DSA-241.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;By using the classical fixed point index theorem for compact maps and the Leggett-Williams fixed point theorem respectively, in this paper, some results of single and multiple positive solutions to a class of nonlinear first-order periodic boundary value problems of impulsive dynamic equations on time scales are obtained. Two examples are given to illustrate the main results in this paper.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">515</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">NASEER AHMAD ASIF</style></author><author><style face="normal" font="default" size="100%">RAHMAT ALI KHAN</style></author><author><style face="normal" font="default" size="100%">JOHNNY HENDERSON</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF POSITIVE SOLUTIONS TO A SYSTEM OF SINGULAR BOUNDARY VALUE PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">34B16</style></keyword><keyword><style  face="normal" font="default" size="100%">34b18</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/28-DSA-29-13.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Existence results for positive solutions of a coupled system of nonlinear singular two point boundary value problems of the type&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; −x ′′(t) = p( t ) f(t, y( t ),&amp;nbsp;x′ (t) ),&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; t ∈ (0, 1),&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; −y ′′(t) = q( t ) g(t, x( t ),&amp;nbsp;y′ (t) ),&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;t ∈ (0, 1),&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; a&lt;sub&gt;1&lt;/sub&gt;x(0) − b&lt;sub&gt;1&lt;/sub&gt;x ′ (0) = x ′ (1) = 0,&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; a&lt;sub&gt;2&lt;/sub&gt;y(0) − b&lt;sub&gt;2&lt;/sub&gt;y ′ (0) = y ′ (1) = 0,&lt;/p&gt;

&lt;p&gt;are established. The nonlinearities f, g : [0, 1] × [0, ∞) × (0, ∞) → [0, ∞) are allowed to be singular at x ′ = 0 and y ′ = 0. The functions p, q ∈ C(0, 1) are positive on (0, 1) and the constants a&lt;sub&gt;i&lt;/sub&gt; , b&lt;sub&gt;i&lt;/sub&gt; (i = 1, 2) &amp;gt; 0. An example is included to show the applicability of our result.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">395</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RUI A. C. FERREIRA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF SOLUTION TO AN INTEGRODYNAMIC EQUATION</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26D10</style></keyword><keyword><style  face="normal" font="default" size="100%">26D15</style></keyword><keyword><style  face="normal" font="default" size="100%">39A12</style></keyword><keyword><style  face="normal" font="default" size="100%">45J05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/21-DSA-264.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We prove existence of solution to an integrodynamic equation on time scales under some suitable conditions on the functions involved. In some particular cases, uniqueness is also demonstrated. Some applications of our results are provided.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">289</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MOUFFAK BENCHOHRA</style></author><author><style face="normal" font="default" size="100%">FARIDA BERHOUN</style></author><author><style face="normal" font="default" size="100%">JUAN J. NIETO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE RESULTS FOR IMPULSIVE BOUNDARY VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/41-DSA-299.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><section><style face="normal" font="default" size="100%">585</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">M. FRIGON</style></author><author><style face="normal" font="default" size="100%">H. GILBERT</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE THEOREMS FOR SYSTEMS OF THIRD ORDER DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A34</style></keyword><keyword><style  face="normal" font="default" size="100%">34A60</style></keyword><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/01-DSA-01.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">23</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we establish the existence of solutions to systems of third order differential equations. A notion of solution-tube to these problems is introduced. This notion extends to systems the notion of upper and lower solutions of third order differential equations. Our proofs rely on the Leray-Schauder degree and the theory of multivalued mappings.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">1</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">T. ABDELJAWAD</style></author><author><style face="normal" font="default" size="100%">D. BALEANULO</style></author><author><style face="normal" font="default" size="100%">F. JARAD</style></author><author><style face="normal" font="default" size="100%">O. G. MUSTAFA</style></author><author><style face="normal" font="default" size="100%">J. J. TRUJILLO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A FITE TYPE RESULT FOR SEQUENTIAL FRACTIONAL DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A08</style></keyword><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/27-DSA-29-12.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Given the solution f of the sequential fractional differential equation&lt;/p&gt;

&lt;p&gt;&lt;sub&gt;a&lt;/sub&gt;D&lt;sup&gt;α&lt;/sup&gt;&lt;sub&gt;t&lt;/sub&gt; (&amp;nbsp;&lt;sub&gt;a&lt;/sub&gt;D&lt;sup&gt;α&lt;/sup&gt;&lt;sub&gt;t&lt;/sub&gt; f ) + P( t ) f = 0, t ∈ [b, c],&amp;nbsp; &amp;nbsp; where&amp;nbsp; &amp;nbsp;−∞ &amp;lt; a &amp;lt; b &amp;lt; c &amp;lt; +∞, α ∈ (1/ 2 , 1)&amp;nbsp; &amp;nbsp; and&amp;nbsp; &amp;nbsp;P : [a, +∞) → [ 0, P&lt;sub&gt;∞&lt;/sub&gt;], P&lt;sub&gt;∞&lt;/sub&gt; &amp;lt; +∞,&amp;nbsp; &amp;nbsp; is continuous. Assume that there exist&amp;nbsp; &amp;nbsp;t&lt;sub&gt;1&lt;/sub&gt;, t&lt;sub&gt;2&lt;/sub&gt; ∈ [b, c]&amp;nbsp; such that&amp;nbsp; f( t&lt;sub&gt;1&amp;nbsp;&lt;/sub&gt;) = (&lt;sub&gt;a&lt;/sub&gt;D&lt;sup&gt;α&lt;/sup&gt;&lt;sub&gt;t &lt;/sub&gt;f )( t&lt;sub&gt;2&amp;nbsp;&lt;/sub&gt;) = 0. Then, we establish here a positive lower bound for c − a which depends solely on α, P&lt;sub&gt;∞&lt;/sub&gt;. Such a result might be useful in discussing disconjugate fractional differential equations and fractional interpolation, similarly to the case of (integer order) ordinary differential equations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">383</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ILKAY YASLAN KARACA</style></author><author><style face="normal" font="default" size="100%">OZLEM YILMAZ</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">FOURTH-ORDER M-POINT BOUNDARY VALUE PROBLEMS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/19-DSA-257.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">21</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let T be a time scale with [a, b] ⊂ T. We establish criteria for existence of one or more than one positive solutions of the non-eigenvalue problem (0.1)    y △4 (t) − q(t)y ∆2 (σ(t)) = f(t, y(t)), t ∈ [a, b] ⊂ T, y(a) = Pm−2 i=1 aiy(ξi), y(σ 2 (b)) = Pm−2 i=1 biy(ξi), y ∆2 (a) = Pm−2 i=1 aiy ∆2 (ξi), y∆2 (σ 2 (b)) = Pm−2 i=1 biy ∆2 (ξi), where ξi ∈ (a, b), ai , bi ∈ [0, ∞) (for i ∈ {1, 2, . . . , m−2}) are given constants. Later, we consider the existence and multiplicity of positive solutions for the eigenvalue problem y △4 (t) − q(t)y ∆2 (σ(t)) = λf(t, y(t)) with the same boundary conditions. We shall also obtain criteria which lead to nonexistence of positive solutions. In both problems, we will use Krasnoselskii fixed point theorem.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">249</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MAREK T. MALINOWSKI</style></author><author><style face="normal" font="default" size="100%">MARIUSZ MICHTA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">FUZZY STOCHASTIC INTEGRAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">03E72</style></keyword><keyword><style  face="normal" font="default" size="100%">37H10</style></keyword><keyword><style  face="normal" font="default" size="100%">60H05</style></keyword><keyword><style  face="normal" font="default" size="100%">60H20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/33-DSA-30-08.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">21</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we propose a new approach to fuzzy stochastic integrals of Itô and Aumann type. Then a fuzzy equation with fuzzy stochastic integrals is investigated. The existence and uniqueness of solution is proven. Some typical properties of the solution are also obtained. Similar results to set-valued stochastic integral equations are stated.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">473</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">HOMOTOPY EXTENSION TYPE MAPS AND FIXED POINTS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/26-DSA-29-11.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">7</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Some new continuation theorems are presented for admissible (and more general) maps using the idea of extendability.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">375</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">K. KROPIELNICKA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">IMPLICIT DIFFERENCE METHODS FOR PARABOLIC FDE ON CYLINDRICAL DOMAINS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/39-DSA-269.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">19</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Implicit difference schemes for quasilinear parabolic functional differential equations are presented. Ben- efits of implicit methods are pointed. The attention is focused here on cylindrical domains. Operators approximating mixed derivatives on irregular grids are introduced. A complete convergence analysis for methods is presented. Nonlinear estimates of the Perron type for given functions with respect to functional variables are used. Results obtained in the paper can be applied to differential integral problems and to equations with deviated variables. Numerical examples display the results of our investigations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">557</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">YANSHENG LIU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">LIDSTONE BOUNDARY VALUE PROBLEMS WITH SIGN-CHANGING NONLINEAR TERMS AND HIGHER ORDER DERIVATIVES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/09-DSA-211.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;By employing topological degree theory, this paper investigates the existence of at least one nontrivial solutions for Lidstone boundary value problems with sign-changing nonlinear term and higher order derivatives. Meanwhile, one example is worked out to demonstrate the main result.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">113</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MOUFFAK BENCHOHRA</style></author><author><style face="normal" font="default" size="100%">DJAMILA SEBA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MEASURE OF NONCOMPACTNESS AND PARTIAL DIFFERENTIAL EQUATIONS INVOLVING RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">26A42</style></keyword><keyword><style  face="normal" font="default" size="100%">34G20</style></keyword><keyword><style  face="normal" font="default" size="100%">34G25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/36-DSA-247.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we prove the existence of mild solutions for an initial value problem for a semilinear differential equation involving the Riemann-Liouville fractional derivative. The technique relies on the concept of measures of noncompactness and Mönch’s fixed point theorem.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">527</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">WAWRZYNIEC SZATANIK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MINIMAL AND MAXIMAL SOLUTIONS FOR INTEGRAL BOUNDARY VALUE PROBLEMS FOR THE SECOND ORDER DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A45</style></keyword><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/07-DSA-133.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper deals with boundary value problems for the second order differential equations with deviating arguments and integral boundary conditions. Sufficient conditions are formulated under which such a problem has at least one solution. A monotone iterative method is used. Example with numerical result is included to illustrate scheme used in the main theorem&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">87</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">A. F. GÜVENILIR</style></author><author><style face="normal" font="default" size="100%">Y. SAHINER</style></author><author><style face="normal" font="default" size="100%">A. ZAFER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MIXED NONLINEAR OSCILLATION OF SECOND ORDER FORCED DYNAMIC EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A11</style></keyword><keyword><style  face="normal" font="default" size="100%">39A13</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/45-DSA-361.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;By using a technique similar to the one introduced by Kong [J. Math. Anal. Appl. 229 (1999) 258–270] and employing an arithmetic-geometric mean inequality, we establish oscillation criteria for second-order forced dynamic equations on time scales containing mixed nonlinearities of the form p(t)x ∆ ∆ + q(t)x σ + Xn i=1 qi(t)|x σ | αi−1x σ = e(t), t ≥ t0 where p, q, qi , e : T → R are right-dense continuous with p &amp;gt; 0, σ is the forward jump operator, x σ (t) := x(σ(t)), and the exponents satisfy α1 &amp;gt; · · · &amp;gt; αm &amp;gt; 1 &amp;gt; αm+1 &amp;gt; · · · αn &amp;gt; 0. The results extend many well-known interval oscillation criteria from continuous case to arbitrary time scales.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">635</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SAID R. GRACE</style></author><author><style face="normal" font="default" size="100%">RAVI P. AGARWAL</style></author><author><style face="normal" font="default" size="100%">WICHUTA SAE-JIE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MONOTONE AND OSCILLATORY BEHAVIOR OF CERTAIN FOURTH ORDER NONLINEAR DYNAMIC EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">34K11</style></keyword><keyword><style  face="normal" font="default" size="100%">39A11</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/02-DSA-02.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Monotone and oscillatory behavior of solutions of the fourth order dynamic equation (a(x ∆∆) α ) ∆∆(t) + q(t)(x σ ) β (t) = 0 with the property that x(t) R t t0 R s t0 a−1/α(τ)∆τ∆s → 0 as t → ∞ are established.&amp;nbsp;&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">25</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">TADEUSZ JANKOWSKI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MULTIPLE SOLUTIONS FOR A CLASS OF BOUNDARY–VALUE PROBLEMS WITH DEVIATING ARGUMENTS AND INTEGRAL BOUNDARY CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/13-DSA-230.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper considers second order differential equations with integral boundary conditions. We establish sufficient conditions under which such boundary value problems with deviating arguments have positive solutions. To obtain the existence of at least three positive solutions, we use a fixed point theorem due to Avery and Peterson&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">179</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">John R. Graef</style></author><author><style face="normal" font="default" size="100%">S. H. SAKER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NEW OSCILLATION CRITERIA FOR GENERALIZED SECOND-ORDER NONLINEAR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K11</style></keyword><keyword><style  face="normal" font="default" size="100%">34K40</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/32-DSA-30-07.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, the authors consider the second-order neutral functional differential equation&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;[ p(t) ψ( y(t) )(x′(t) )&lt;sup&gt;γ&lt;/sup&gt; ] ′ + q(t) f( y(δ(t)) ) = 0,&amp;nbsp; &amp;nbsp;t ≥ t&lt;sub&gt;0&lt;/sub&gt;,&lt;/p&gt;

&lt;p&gt;where&amp;nbsp; &amp;nbsp;x(t) = y(t) + r(t) y( τ(t) )&amp;nbsp; and&amp;nbsp; γ &amp;gt; 0&amp;nbsp; is a ratio of odd positive integers. They establish some new sufficient conditions for oscillation of all solutions that are substantial improvements to some existing results in the literature. Some examples are included to illustrate the main results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">455</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">WENJUN LIU</style></author><author><style face="normal" font="default" size="100%">QUÔC A NGÔ</style></author><author><style face="normal" font="default" size="100%">WENBING CHEN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON NEW OSTROWSKI TYPE INEQUALITIES FOR DOUBLE INTEGRALS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26D15</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A12</style></keyword><keyword><style  face="normal" font="default" size="100%">39A13</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/14-DSA-237.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A new Ostrowski type inequality for double integrals on time scales via ∆∆-integral is derived which unify corresponding continuous and discrete versions. Analogous results for ∇∇-, ∆∇- and ∇∆-integrals are also discussed.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">189</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">PAVEL REHAK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NEW RESULTS ON CRITICAL OSCILLATION CONSTANTS DEPENDING ON A GRAININESS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A11</style></keyword><keyword><style  face="normal" font="default" size="100%">39A12</style></keyword><keyword><style  face="normal" font="default" size="100%">39A13</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/20-DSA-262.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We establish criteria of Hille-Nehari type for the half-linear second order dynamic equation ( r(t) Φ(y &lt;sup&gt;∆&lt;/sup&gt;))&lt;sup&gt;∆&lt;/sup&gt; +p(t) Φ (y &lt;sup&gt;σ&lt;/sup&gt; )= 0, Φ (u) = |u|&lt;sup&gt;α−1&lt;/sup&gt; sgn u, α &amp;gt; 1, on time scales, under the condition R∞ r 1/(1−α) (s) ∆s &amp;lt; ∞. As a particular important case we get that there is a (non-improvable) critical oscillation constant which may be different from the one known from the continuous case, and its value depends on the graininess of a time scale and on the coefficient r. Along with the results of the previous paper by the author, which dealt with the condition R∞ r &lt;sup&gt;1/(1−α)&lt;/sup&gt; (s) ∆s = ∞, a quite complete discussion on generalized Hille-Nehari type criteria involving the best possible constants is provided. To prove these criteria, appropriate modifications of the approaches known from the linear case (α = 2) or the continuous case (T = R) cannot be used in a general case, and thus we apply a new method. As applications of the main results we state criteria for strong (non)oscillation, examine a generalized Euler type equation, and establish criteria of Kneser type. Examples from q-calculus and h-calculus, and a Hardy type inequality are presented as well. Our results unify and extend many existing results from special cases, and are new even in the well-studied discrete case.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">271</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">QINGKAI KONG</style></author><author><style face="normal" font="default" size="100%">XIAOFEI WANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NONLINEAR INITIAL VALUE PROBLEMS WITH p-LAPLACIAN</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A12</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/03-DSA-03.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study the nonlinear initial value problem consisting of the equation − [ p(t) φ(y′ ) ]′ +&amp;nbsp;q(t) φ(y) = w(t) f(y) with φ(y) = |y|&lt;sup&gt;r−1&lt;/sup&gt;y for r &amp;gt; 0 and the initial conditions y(t&lt;sub&gt;0&lt;/sub&gt;) = y&lt;sub&gt;0&lt;/sub&gt;, (p&lt;sup&gt;1/r&amp;nbsp;&lt;/sup&gt;y′ ) (t&lt;sub&gt;0&lt;/sub&gt;) = z&lt;sub&gt;0&lt;/sub&gt;. By establishing nonlinear integral inequalities and applying a generalized energy function and a generalized Pr¨ufer transformation, we prove that the solution of this initial value problem exists on the whole domain and is unique. This paper provides a foundation for a forthcoming paper on the existence of nodal solutioins of second order nonlinear boundary value problems with p-Laplacian.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">33</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">N. C. APREUTESEI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OPTIMAL CONTROL FOR PREDATOR-PREY SYSTEM WITH PREY-DEPENDENT FUNCTIONAL RESPONSE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34H05</style></keyword><keyword><style  face="normal" font="default" size="100%">49K15</style></keyword><keyword><style  face="normal" font="default" size="100%">92D25</style></keyword><keyword><style  face="normal" font="default" size="100%">93C10</style></keyword><keyword><style  face="normal" font="default" size="100%">93C15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/37-DSA-249.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;An optimal control problem is studied for a predator-prey system with logistic growth rate of the prey and a prey-dependent functional response of the predator. The control function has two components and signifies the rate of mixture between the individuals of the species. The form of the optimal control is determined according to Pontryagin’s maximum principle. It is bang-bang and the number of switchings points depends on the choice of some specific parameters.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">537</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MASNITA MISIRAN</style></author><author><style face="normal" font="default" size="100%">CHANGZI WU</style></author><author><style face="normal" font="default" size="100%">ZUDI LU</style></author><author><style face="normal" font="default" size="100%">K. L. TEO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OPTIMAL FILTERING OF LINEAR SYSTEM DRIVEN BY FRACTIONAL BROWNIAN MOTION</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">41A50</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/34-DSA-30-09.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">19</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we consider a continuous time filtering of a multi-dimensional Langevin stochastic differential system driven by a fractional Brownian motion process. It is shown that this filtering problem is equivalent to an optimal control problem involving convolutional integrals in its dynamical system. Then, a novel approximation scheme is developed and applied to this optimal control problem. It yields a sequence of standard optimal control problems. The convergence of the approximate standard optimal control problem to the optimal control problem involving convolutional integrals in its system dynamics is established. Two numerical examples are solved by using the method proposed. The results obtained clearly demonstrate its efficiency and effectiveness.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">495</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RUN XU</style></author><author><style face="normal" font="default" size="100%">FANWEI MENG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OSCILLATION CRITERIA FOR SECOND ORDER NEUTRAL PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/18-DSA-248.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;. Some new oscillation criteria are established for second order neutral partial functional differential equation of the form ∂ ∂t &quot; r(t) ∂ ∂t u(x, t) +X l i=1 λi(t)u(x, t − τi) !#= a(t)△u(x, t) +Xs k=1 ak(t)△u(x, t − ρk(t)) − q(x, t)u(x, t) − Xm j=1 qj (x, t)fj (u(x, t − σj )), (x, t) ∈ Ω × [0, ∞) ≡ G under the conditions R∞ t0 r −1 (s)ds = ∞ and R∞ t0 r −1 (s)ds &amp;lt; ∞, respectively. where Ω is a bounded domain in RN with a piecewise smooth boundary ∂Ω and △ is the laplacian in the Euclidean N−space RN .&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">235</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MUSTAFA KEMAL YILDIZ</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OSCILLATION OF NONLINEAR NEUTRAL DELAY DIFFERENTIAL EQUATION WITH SEVERAL COEFFICIENTS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">34K40</style></keyword><keyword><style  face="normal" font="default" size="100%">34K99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/15-DSA-239.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this article, we show that the oscillation of all solutions to the neutral equation [x (t) − R (t) N (x (t − κ))]′ + Xn i=1 Pi (t) Fi (x (t − τi)) − Xm j=1 Qj (t) Gj (x (t − σj )) = 0 is implied by the oscillation of all solutions to the linear equation [x (t) − rx (t − κ)]′ + Xn i=1 pix (t − τi) − Xm j=1 qjx (t − σj ) = 0. In these equations, R,Pi , Qj are positive and continuous functions, and κ, τi , σj are positive constants that represent delays&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">199</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">I. O. ISAAC</style></author><author><style face="normal" font="default" size="100%">Z. LIPSCEY</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OSCILLATIONS OF SCALAR NEUTRAL IMPULSIVE DIFFERENTIAL EQUATIONS OF THE FIRST ORDER WITH VARIABLE COEFFICIENTS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/04-DSA-04.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The theory of oscillations of neutral impulsive differential equations is gradually occupying a central place among the theories of oscillations of impulsive differential equations. This could be due to the fact that neutral impulsive differential equations play fundamental roles in the present drive to further develop information technology. Indeed, neutral differential equations appear in networks containing lossless transmission lines (as in high-speed computers where the lossless transmission lines are used to interconnect switching circuits). In this paper, we generalize and prove the results of oscillations of neutral delay differential equations with constant coefficients obtained by Gyori and Ladas for impulsive differential equations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">45</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">CAI-XUN WANG</style></author><author><style face="normal" font="default" size="100%">HONG-RUI SUN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR THIRD-ORDER THREE-POINT NONHOMOGENEOUS BOUNDARY VALUE PROBLEM</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/17-DSA-244.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we establish the existence or nonexistence of positive solutions for singular third-order three-point nonhomogeneous boundary value problem. First, we give a new form of the solution, and then, some useful properties of the Green’s function are obtained by a new method. Finally, we employ a cone theoretic fixed-point index theorem to establish our results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">225</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">J. HARJANI</style></author><author><style face="normal" font="default" size="100%">B. LOPEZ</style></author><author><style face="normal" font="default" size="100%">K. SADARANGANI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON POSITIVE SOLUTIONS OF A NONLINEAR FOURTH ORDER BOUNDARY VALUE PROBLEM VIA A FIXED POINT THEOREM IN ORDERED SETS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34b18</style></keyword><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/44-DSA-357.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper presents sufficient conditions for the existence and uniqueness of a positive solution to a nonlinear fourth-order differential equation under Lidstone boundary conditions. Our analysis relies on a fixed point theorem in partially ordered sets.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">625</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ANTONIN SLAVIK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">PRODUCT INTEGRATION ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A42</style></keyword><keyword><style  face="normal" font="default" size="100%">28B10</style></keyword><keyword><style  face="normal" font="default" size="100%">34A30</style></keyword><keyword><style  face="normal" font="default" size="100%">39A12</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/08-DSA-190.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We introduce the notion of product ∆-integral of a matrix function defined on an arbitrary time scale, and thus generalize the classical definition of product integral. We prove that every Riemann ∆-integrable matrix function is also product ∆-integrable, and investigate the properties of the indefinite product ∆-integral, including its relation to linear systems of dynamic equations. Finally, we generalize the notion of the matrix exponential function.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">97</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">YUHU WU</style></author><author><style face="normal" font="default" size="100%">XIAOPING XUE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SHADOWING PROPERTY FOR INDUCED SET-VALUED DYNAMICAL SYSTEMS OF SOME EXPANSIVE MAPS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">28B20</style></keyword><keyword><style  face="normal" font="default" size="100%">37C15</style></keyword><keyword><style  face="normal" font="default" size="100%">37F15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/29-DSA-30-02.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we study the shadowing property for induced set-valued dynamical systems of some expansive maps. We show that if f is a positively expansive open map, then the induced map F has shadowing property. We introduce the notion of ball expansive maps, and show that such maps have shadowing property.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">405</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BARUCH CAHLON</style></author><author><style face="normal" font="default" size="100%">DARRELL SCHMIDT</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STABILITY CRITERIA FOR CERTAIN SECOND ORDER NEUTRAL DELAY DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34D99</style></keyword><keyword><style  face="normal" font="default" size="100%">45E99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/25-DSA-29-10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">22</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we study the asymptotic stability of the zero solution of second order neutral delay differential equation of the form&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;y ′′(t) + αy′′(t − τ) + ay′ (t) + by′ (t − τ) + cy(t) + dy(t − τ) = 0,&lt;/p&gt;

&lt;p&gt;where a, b, c, d, α ∈ (−1, 0)∪(0, 1), and τ &amp;gt; 0 are constants. In this paper, we obtain a new necessary condition and obtain robust method of determining whether the zero solution is asymptotically stable. In proving our results we make use of Pontryagin’s theory for quasi-polynomials.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">353</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">B. C. DHAGE</style></author><author><style face="normal" font="default" size="100%">John R. Graef</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON STABILITY OF ABSTRACT MEASURE DELAY INTEGRO-DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34G99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/23-DSA-29-08.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, an existence as well as an existence and uniqueness result are proved for an abstract measure delay integro-differential equation. The extendability and stability of solutions are also discussed. An illustrative example is included.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">323</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MARTIN BOHNER</style></author><author><style face="normal" font="default" size="100%">GUSEIN SH. GUSEINOV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SURFACE AREAS AND SURFACE INTEGRALS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26B15</style></keyword><keyword><style  face="normal" font="default" size="100%">28A75</style></keyword><keyword><style  face="normal" font="default" size="100%">34N05</style></keyword><keyword><style  face="normal" font="default" size="100%">39A12</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/31-DSA-30-05.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">19</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study surfaces parametrized by time scale parameters, obtain an integral fomula for computing the area of time scale surfaces, introduce delta integrals over time scale surfaces, and give sufficient conditions that ensure existence of these integrals.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">435</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">CHUFEN WU</style></author><author><style face="normal" font="default" size="100%">PEIXUAN WENG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">TRAVELING WAVEFRONTS FOR A SIS EPIDEMIC MODEL WITH STAGE STRUCTURE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35K57</style></keyword><keyword><style  face="normal" font="default" size="100%">92D30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/10-DSA-217.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">21</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A SIS epidemic model with stage structure is studied. The existence of traveling wavefronts is shown by using the technique of weak upper and lower solutions and Schauder fixed point theorem.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">125</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ALEXANDER J. ZASLAVSKI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A TURNPIKE PROPERTY FOR A CLASS OF DISCRETE-TIME OPTIMAL CONTROL SYSTEMS AND POROSITY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In the paper we investigate the structure of solutions of discrete-time control systems with a compact metric space of states. We are interested in turnpike properties of the approximate solutions which are independent of the length of the interval, for all sufficiently large intervals. Using the porosity notion we show that most control systems possess the turnpike property.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">303</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">V. JIMÉNEZ LÓPEZ</style></author><author><style face="normal" font="default" size="100%">J. KUPKA</style></author><author><style face="normal" font="default" size="100%">A. LINERO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE ω-LIMIT SETS OF PRODUCT MAPS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">37B99</style></keyword><keyword><style  face="normal" font="default" size="100%">37E05</style></keyword><keyword><style  face="normal" font="default" size="100%">37E99</style></keyword><keyword><style  face="normal" font="default" size="100%">54H20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/47-DSA-182.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let ω(·)&amp;nbsp; denote the union of all ω-limit sets of a given map. As the main result of this paper we prove that, for given continuous interval maps f&lt;sub&gt;1&lt;/sub&gt;, . . . , f&lt;sub&gt;m&lt;/sub&gt;, the union of all ω-limit sets of the product map f&lt;sub&gt;1&lt;/sub&gt; × · · · × fm and the cartesian product of the sets ω(f&lt;sub&gt;1&lt;/sub&gt;), . . . , ω(f&lt;sub&gt;m&lt;/sub&gt;) coincide. This result enriches the theory of multidimensional permutation product maps, i.e., maps of the form F( x&lt;sub&gt;1&lt;/sub&gt;, . . . , x&lt;sub&gt;m&amp;nbsp;&lt;/sub&gt;) = ( f&lt;sub&gt;σ(1) &lt;/sub&gt;(x&lt;sub&gt;σ(1)&lt;/sub&gt;), . . . , f&lt;sub&gt;σ(m)&lt;/sub&gt;(x&lt;sub&gt;σ(m)&lt;/sub&gt;) ), where σ is a permutation of the set of indices {1, . . . , m}. For any such map F, we prove that the set ω(F) is closed and we also show that ω(F) cannot be a proper subset of the center of the map F. These results solve open questions mentioned, e.g., in [ F. Balibrea, J. S. Cánovas, A. Linero, New results on topological dynamics of antitriangular maps, Appl. Gen. Topol.].&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">667</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MICHAEL GIL</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ABSOLUTE AND INPUT-TO-STATE STABILITIES OF NONAUTONOMOUS SYSTEMS WITH CAUSAL MAPPINGS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K20</style></keyword><keyword><style  face="normal" font="default" size="100%">34K99</style></keyword><keyword><style  face="normal" font="default" size="100%">93D05</style></keyword><keyword><style  face="normal" font="default" size="100%">93D25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/43-DSA-210.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider systems governed by the scalar equation Xn k=0 ak(t)x (n−k) (t) = [Fx](t) (t ≥ 0), where a0 ≡ 1; ak(t) (k = 1, . . ., n) are positive continuous functions and F is a causal mapping. We also consider the case when F depends on the input. Such equations include differential, integrodifferential and other traditional equations. It is assumed that all the roots rk(t) (k = 1, . . ., n) of the polynomial z n + a1(t)z n−1 + · · · + an(t) are real and negative for all t ≥ 0. Exact explicit conditions for the absolute and input-to-state stabilities of the considered systems are established.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">655</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BAPURAO  DHAGE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">APPLICABLE FIXED POINT THEORY IN FUNCTIONAL DIFFERENTIAL EQUATIONS ON UNBOUNDED INTERVALS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/47-DSA-227.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">24</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this article, we discuss the applications of some fixed point theorems to various types of functional differential equations for proving the existence as well as global attractivity and ultimate positivity of solutions on unbounded intervals under some usual natural conditions. Our hypotheses and claims have also been explained with the help of some natural realizations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">701</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">R. SAKTHIVEL</style></author><author><style face="normal" font="default" size="100%">E. R. ANANDHI</style></author><author><style face="normal" font="default" size="100%">SANG-GU LEE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">APPROXIMATE CONTROLLABILITY OF IMPULSIVE DIFFERENTIAL INCLUSIONS WITH NONLOCAL CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34G20</style></keyword><keyword><style  face="normal" font="default" size="100%">93B05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/42-DSA-208.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In order to describe various real-world problems in physical and engineering sciences that are subject to abrupt changes at certain instants during the evolution process, impulsive differential equations has been used to describe the system model. In this article, the problem of approximate controllability for nonlinear impulsive neutral differential inclusions with nonlocal conditions is studied under the assumption that the corresponding linear control system is approximately controllable. Using a fixed point theorem for condensing multi-valued maps and semigroup theory, sufficient conditions are formulated and proved. Finally, an example is provided to illustrate the results obtained.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">637</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">R. RAUTMANN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">BLOW UP IN A CLASS OF NON-AUTONOMOUS DYNAMIC SYSTEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A12</style></keyword><keyword><style  face="normal" font="default" size="100%">34A40</style></keyword><keyword><style  face="normal" font="default" size="100%">34C11</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/01-DSA-CY-1-Rautmann.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;For a class of non-autonomous dynamic systems in the positive cone R&lt;sup&gt;n&lt;/sup&gt;&lt;sub&gt;+&lt;/sub&gt;&amp;nbsp; of&amp;nbsp; R&lt;sup&gt;n&lt;/sup&gt; we prove the blow up of all solutions having sufficiently large initial values. To more specialized nonautonomous systems we present explicit lower and upper bounds for solutions as well as for the time of their blowing up.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">1</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ALFONSO C. CASAL</style></author><author><style face="normal" font="default" size="100%">J. ILDEFONSO DIAZ</style></author><author><style face="normal" font="default" size="100%">JOSE M. VEGAS</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">BLOW-UP IN SOME ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS WITH TIME-DELAY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K05</style></keyword><keyword><style  face="normal" font="default" size="100%">34K12</style></keyword><keyword><style  face="normal" font="default" size="100%">34K40</style></keyword><keyword><style  face="normal" font="default" size="100%">35B05</style></keyword><keyword><style  face="normal" font="default" size="100%">35B30</style></keyword><keyword><style  face="normal" font="default" size="100%">35B40</style></keyword><keyword><style  face="normal" font="default" size="100%">35B60</style></keyword><keyword><style  face="normal" font="default" size="100%">35B65</style></keyword><keyword><style  face="normal" font="default" size="100%">35K55</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/03-DSA-CY-3-Casal.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Blow-up phenomena are analyzed for both the delay-differential equation (DDE) u ′ (t) = B ′ (t)u(t − τ), and the associated parabolic PDE (PDDE) ∂tu = ∆u + B ′ (t)u(t − τ, x), where B : [0, τ] → R is a positive L 1 function which behaves like 1/ |t − t ∗ | α , for some α ∈ (0, 1) and t ∗ ∈ (0, τ). Here B′ represents its distributional derivative. For initial functions satisfying u(t ∗ − τ) &amp;gt; 0, blow up takes place as t ր t ∗ and the behavior of the solution near t ∗ is given by u(t) ≃ B(t)u(t − τ), and a similar result holds for the PDDE. The extension to some nonlinear equations is also studied: we use the Alekseev’s formula (case of nonlinear (DDE)) and comparison arguments (case of nonlinear (PDDE)). The existence of solutions in some generalized sense, beyond t = t ∗ is also addressed. This results is connected with a similar question raised by A. Friedman and J. B. McLeod in 1985 for the case of semilinear parabolic equations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">29</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">PHILIP W. SCHAEFER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">BLOW-UP PHENOMENA IN SOME POROUS MEDIUM PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35K57</style></keyword><keyword><style  face="normal" font="default" size="100%">35K60</style></keyword><keyword><style  face="normal" font="default" size="100%">35K65</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/08-DSA-CY-8-Schaefer.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">7</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider a Dirichlet type initial-boundary value problem for the porous medium equation with a power function reaction term. We determine a condition on the initial data which ensures blow-up of the solution in finite time and an upper bound for the blow-up time. We also discuss when blow-up does not occur and a more general initial-boundary value problem where blow-up does occur.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">103</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JAN ANDRES</style></author><author><style face="normal" font="default" size="100%">LUISA MALAGUTI</style></author><author><style face="normal" font="default" size="100%">VALENTINA TADDEI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON BOUNDARY VALUE PROBLEMS IN BANACH SPACES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A60</style></keyword><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">34C25</style></keyword><keyword><style  face="normal" font="default" size="100%">47H09</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/22-DSA-118.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">27</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The paper deals with boundary value problems associated to first-order differential inclusions in Banach spaces. The solvability is investigated in the (strong) Carath´eodory sense on compact intervals. To this aim, we develop a general method that relies on degree arguments. This method is still combined with a bound sets technique for checking the behavior of trajectories in the neighborhood of a suitable parametric set of candidate solutions. On this basis, we obtain effective criteria for the existence of solutions of Floquet problems. The existence of entirely bounded solutions is also established by means of a sequence of solutions on compact increasing intervals.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">275</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JOSEF DIBLIK</style></author><author><style face="normal" font="default" size="100%">IRENA HLAVICKOVA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">COMBINATION OF LIAPUNOV AND RETRACT METHODS IN THE INVESTIGATION OF THE ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF SYSTEMS OF DISCRETE EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A11</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/35-DSA-183.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">31</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This contribution is devoted to a discussion of the asymptotic behavior of solutions of systems of first order nonlinear difference equations. We show that under appropriate conditions there exists at least one solution of the system considered the graph of which stays in a prescribed domain. The domains we work with are the so called polyfacial sets. In literature, retract and Liapunov type approaches are known as excellent asymptotic analysis tools. We present a method which connects both these techniques. Thanks to this, the achieved result can be applied to a substantially wider range of equations. The main result is applied to study a linear system of difference equations as well as to investigate a nonlinear system similar to the discrete scalar equation of Bernoulli’s type. Results are illustrated by detailed examples.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">507</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ARTURO DE PABLO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">CRITICAL COEFFICIENTS IN BLOW-UP PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35B33</style></keyword><keyword><style  face="normal" font="default" size="100%">35B35</style></keyword><keyword><style  face="normal" font="default" size="100%">35K55</style></keyword><keyword><style  face="normal" font="default" size="100%">35K65</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/07-DSA-CY-7-Pablo.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">22</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We review some problems in the blow-up theory from the point of view of the coefficients involved. In particular we are interested in problems in which a competition of two opposed terms produces different behaviours; in the critical case of a balance of both terms we study the influence of a coefficient in one of them. Existence of stationary solutions or self-similar solutions plays a fundamental role.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">81</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">AGNIESZKA B. MALINOWSKA</style></author><author><style face="normal" font="default" size="100%">DELFIM TORRES</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE DIAMOND-ALPHA RIEMANN INTEGRAL AND MEAN VALUE THEOREMS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A42; 39A12</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/33-DSA-173.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study diamond-alpha integrals on time scales. A diamond-alpha version of Fermat’s theorem for stationary points is also proved, as well as Rolle’s, Lagrange’s, and Cauchy’s mean value theorems on time scales.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">469</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">QIN SHENG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">AN EFFECTIVE SEMI-IMPLICIT METHOD FOR CIRCULARLY SYMMETRIC QUENCHING OPTICAL WAVES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A13</style></keyword><keyword><style  face="normal" font="default" size="100%">74H15</style></keyword><keyword><style  face="normal" font="default" size="100%">74S20</style></keyword><keyword><style  face="normal" font="default" size="100%">: 34A45</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/12-DSA-CY-11-Sheng.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Recent electro-optical studies indicate that the spatial profile of a quenching, or collapsing, optical wave evolves to a specific circularly symmetric shape, known as the Townes profile, for elliptically shaped or randomly distorted input beams. Computations of such a Townes profile have been playing an important role in understanding of the wave collapse phenomenon, but the numerical procedures are sensitive due to features of the generalized nonlinear Schr¨odinger equation boundary value problems involved. This paper studies an effective semi-implicit finite difference method equipped with a dynamic shooting strategy for the numerical solution of the quenching optical boundary value problems. The numerical method proposed is simple in structure, easy to use, and weakly asymptotically stable. Simulated circularly symmetric quenching optical waves are given&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">129</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">C. Y. CHAN</style></author><author><style face="normal" font="default" size="100%">P. TRAGOONSIRISAK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EFFECTS OF A CONCENTRATED NONLINEAR SOURCE ON QUENCHING IN R N</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35K57</style></keyword><keyword><style  face="normal" font="default" size="100%">35K60</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/04-DSA-CY-4-ChanTragoonsirisak.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">7</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;. Let T and α be positive real numbers, β be a real number, B be a N-dimensional ball  x ∈ R N : |x| &amp;lt; R centered at the origin with a radius R, and ∂B be its boundary. Also, let ν(x) denote the unit inward normal at x ∈ ∂B, and χB(x) be the characteristic function, which is 1 for x ∈ B, and 0 for x ∈ R N \ B. This article studies the following parabolic Cauchy problem with a concentrated nonlinear source on ∂B: ut − 4u = α(1 + |x|) β ∂χB(x) ∂ν f(u) in R N × (0, T], u(x, 0) = 0 for x ∈ R N , u(x, t) → 0 as |x| → ∞ for 0 &amp;lt; t ≤ T, where f is a given function such that limu→c− f(u) = ∞ for some positive constant c, and f(u) and its derivatives f 0 (u) and f 00(u) are positive for 0 ≤ u &amp;lt; c. It is shown that the solution u always quenches for N ≤ 2, and quenching can be prevented for any β for N ≥ 3. For given R and β, the effects of α on quenching are discussed. Similarly for a given α, the effects of R and β on quenching are investigated.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">47</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JONG  PARK</style></author><author><style face="normal" font="default" size="100%">JUNG  KIM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE AND UNIFORM DECAY FOR A NONLINEAR VISCOELASTIC EQUATION WITH STRONG DAMPING AND NONLINEAR BOUNDARY MEMORY DAMPING TERM</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35L90</style></keyword><keyword><style  face="normal" font="default" size="100%">74DXX</style></keyword><keyword><style  face="normal" font="default" size="100%">93D20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/40-DSA-195.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we prove the existence of the solution to the nonlinear viscoelastic equation with strong damping and nonlinear boundary memory damping term. Moreover, we discuss the uniform decay of the solution&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">605</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">I. J. CABRERA</style></author><author><style face="normal" font="default" size="100%">K. B. SADARANGANI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF SOLUTIONS OF A NONLINEAR INTEGRAL EQUATION ON AN UNBOUNDED INTERVAL</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H09</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/37-DSA-186.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">19</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we investigate a nonlinear integral equation of Volterra type on an unbounded interval. We show that under some assumptions our equation has solutions belonging to the space of bounded and continuous functions on R&lt;sub&gt;+&lt;/sub&gt;. The main tool used in our study is the technique associated with the measures of noncompactness.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">551</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">W. Y. CHAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF THE CLASSICAL SOLUTION FOR DEGENERATE QUASILINEAR PARABOLIC PROBLEMS WITH SLOW DIFFUSIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35K55</style></keyword><keyword><style  face="normal" font="default" size="100%">35K57</style></keyword><keyword><style  face="normal" font="default" size="100%">35K60</style></keyword><keyword><style  face="normal" font="default" size="100%">35K65</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/06-DSA-CY-6-wyChan.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let T ≤ ∞, b be a positive number, m be a positive number such that m &amp;gt; 1, and q be a nonnegative number. Existence and uniqueness of a classical solution are studied for the following degenerate quasilinear parabolic problem,&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; x&lt;sup&gt;q&lt;/sup&gt;u&lt;sub&gt;t &lt;/sub&gt;= ( u&lt;sup&gt;m&amp;nbsp;&lt;/sup&gt;)&lt;sub&gt;xx &lt;/sub&gt;+ bf( u )&amp;nbsp; in (0, 1) × (0, T),&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;u( x, 0 )= u&lt;sub&gt;0&lt;/sub&gt;( x ) in [0, 1], u (0, t) = 0 = u ( 1, t ) for t ∈ (0, T),&lt;/p&gt;

&lt;p&gt;where u&lt;sub&gt;0&lt;/sub&gt;( x ) is a positive function for 0 &amp;lt; x &amp;lt; 1,&amp;nbsp; u&lt;sub&gt;0&lt;/sub&gt;&lt;sup&gt;m&lt;/sup&gt;( x ) ∈ C&lt;sup&gt;2+α&lt;/sup&gt; ( [0, 1] ) for some α ∈ ( 0, 1 ), u&lt;sub&gt;0&lt;/sub&gt;( 0 ) = u&lt;sub&gt;0&lt;/sub&gt;( 1 ) = 0,&amp;nbsp; and f (u) is a given function such that f (0) ≥ 0 and f′ (u) ≥ 0 for u ≥ 0. Furthermore, a criterion for u to blow up in a finite time is given.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">63</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">YUJI LIU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE RESULTS FOR SOLUTIONS OF BVPS OF SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATIONS ON A HALF LINE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">34B37</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/28-DSA-158.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper deals with a class of boundary value problems of the second order impulsive differential equations on a half line. Sufficient conditions are established for the existence of at least one solution of these problems. Our method is based upon the fixed point theorem in Banach spaces. An Example is presented to illustrate the efficiency of the obtained results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">393</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MOHAMED   DARWISH</style></author><author><style face="normal" font="default" size="100%">SOTIRIS  NTOUYAS</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">FUNCTIONAL DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER WITH STATE-DEPENDENT DELAY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">26A42</style></keyword><keyword><style  face="normal" font="default" size="100%">34K30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/36-DSA-185.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we study the existence of solutions for the initial value problem for functional differential equations, as well as, for neutral functional differential equations of fractional order with state-dependent delay. The nonlinear alternative of Leray-Schauder type is the main tool in our analysis.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">539</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">CHENGHUI ZHANG</style></author><author><style face="normal" font="default" size="100%">XIANFU ZHANG</style></author><author><style face="normal" font="default" size="100%">XINZHI LIU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">GLOBAL STABILIZATION OF UNCERTAIN NONLINEAR TIME-DELAY SYSTEMS BY OUTPUT FEEDBACK</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">93C10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/15-DSA-28-04.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, constructive control techniques have been proposed for controlling strict feedback (lower triangular form) nonlinear systems with a time delay in the state. The uncertain nonlinearities are assumed to be bounded by functions of the output multiplied by unmeasured states or delayed states. Based on the using of a linear dynamic high gain observer in combination with a linear dynamic high gain controller, the delay-independent output feedback controller making the closed-loop system globally asymptotically stable (GAS) is explicitly constructed. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">179</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">HONGLEI XU</style></author><author><style face="normal" font="default" size="100%">YUANQIANG CHEN</style></author><author><style face="normal" font="default" size="100%">KOK LAY TEO</style></author><author><style face="normal" font="default" size="100%">RYAN LOXTON</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">AN IMPULSIVE STABILIZING CONTROL OF A NEW CHAOTIC SYSTEM</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34D20</style></keyword><keyword><style  face="normal" font="default" size="100%">34K35</style></keyword><keyword><style  face="normal" font="default" size="100%">93C10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/19-DSA-28-08.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we design a novel impulsive control law to stabilize a new class of chaotic systems. Using a non-quadratic Lyapunov function candidate and a stability theorem in [10], we derive some algebraic sufficient conditions which ensure the asymptotical stability of the chaotic system under the impulsive control strategy. Finally, a numerical example is presented to illustrate the validity of our results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">241</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">HENG-YOU LAN</style></author><author><style face="normal" font="default" size="100%">JUAN J. NIETO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON INITIAL VALUE PROBLEMS FOR FIRST-ORDER IMPLICIT IMPULSIVE FUZZY DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26E50</style></keyword><keyword><style  face="normal" font="default" size="100%">34A10</style></keyword><keyword><style  face="normal" font="default" size="100%">47E05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/45-DSA-219.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">19</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, by using Banach contraction mapping principle theorem, we obtain some new existence and uniqueness theorems of solutions for a new class of initial value problems of first-order implicit impulsive fuzzy differential equations in the metric space of normal fuzzy convex sets with distance given by maximum of the Hausdorff distance between level sets.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">677</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">XIAOCHENG HUANG</style></author><author><style face="normal" font="default" size="100%">ZHITING XU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">KAMENEV-TYPE AND INTERVAL OSCILLATION THEOREMS FOR SECOND ORDER NONLINEAR DELAY DYNAMIC EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10. 34K11</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/38-DSA-189.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;By means of the generalized Riccati technique, we establish Kamenev-type and interval oscillation theorems for the second-order nonlinear delay dynamic equation&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; ( r(t) x&lt;sup&gt;∆&lt;/sup&gt;(t) )&lt;sup&gt;∆&lt;/sup&gt; + p(t) f( x(τ(t)) ) = 0&amp;nbsp;&lt;/p&gt;

&lt;p&gt;on an unbounded time scale T. Our results are extensions of those for second order ordinary differential equations and provide new oscillation criteria for second order delay difference and q-difference equations. Some examples are given to illustrate the significance of our main theorems.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">571</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">QINGKAI KONG</style></author><author><style face="normal" font="default" size="100%">QI-RU WANG</style></author><author><style face="normal" font="default" size="100%">ZHI-QIANG ZHU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">KAMENEV-TYPE OSCILLATION CRITERIA FOR SECOND-ORDER MATRIX DYNAMIC EQUATIONS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A12</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/30-DSA-163.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider the second order matrix valued dynamic equation ( P(t) X&lt;sup&gt;∆&lt;/sup&gt;(t) )&lt;sup&gt;∆&lt;/sup&gt; + Q(t) X( σ(t) ) = 0 on a time scale T, where P, Q ∈ C&lt;sub&gt;rd&lt;/sub&gt;(T, R&lt;sup&gt;n×n&lt;/sup&gt; ) with P(t) positive definite and Q(t) Hermitian on T. Kamenev type criteria and interval criteria are established. Our results cover those for matrix differential equations and provide new oscillation criteria for matrix difference equations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">423</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ADINA OPRISAN</style></author><author><style face="normal" font="default" size="100%">ANDRZEJ KORZENIOWSKI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">LARGE DEVIATIONS FOR ERGODIC PROCESSES IN SPLIT SPACES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">60B10</style></keyword><keyword><style  face="normal" font="default" size="100%">60F10</style></keyword><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/39-DSA-194.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study a family of stochastic additive functionals of Markov processes with locally independent increments switched by jump Markov processes in an asymptotic split phase space. Based on an average approximation, we obtain a large deviation result for this stochastic evolutionary system using a weak convergence approach. Examples, including compound Poisson processes, illustrate cases in which the rate function is calculated in an explicit form.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">589</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JEFFREY R. ANDERSON</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">LONG-TIME BEHAVIOR OF SOLUTIONS OF A NONLINEAR DIFFUSION MODEL WITH TRANSMISSION BOUNDARY CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35B05</style></keyword><keyword><style  face="normal" font="default" size="100%">35K65</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/09-DSA-CY-9-Anderson.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In order to accurately simulate the transport of growth factor from tumor site into a nearby capillary wall, a recently introduced model of tumor-induced capillary growth incorporates a new form of transmission boundary flux. Growth factor emitted from the tumor may be viewed as a diffusible chemical moving through intersticial space, which is represented as a porous medium. Transmission between the capillary wall and intersticial space gives rise to a type of continuous delay/memory condition at the boundary. Herein, we establish results on global solvability and blow up in finite time for a general nonlinear diffusion model, including such transmission boundary conditions. Although the model appears more closely aligned with models involving nonlinear flux conditions at the boundary, these results bear notable similarities to those with Dirichlet boundary conditions.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">111</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">N. G. MEDHIN</style></author><author><style face="normal" font="default" size="100%">WEI WAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MULTI-NEW PRODUCT COMPETITION IN DUOPOLY: A DIFFERENTIAL GAME ANALYSIS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">91A23</style></keyword><keyword><style  face="normal" font="default" size="100%">91A80</style></keyword><keyword><style  face="normal" font="default" size="100%">91B50</style></keyword><keyword><style  face="normal" font="default" size="100%">91B60</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/14-DSA-28-01.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We use a differential game approach to study some aspects of the dynamics and competition in marketing. A market is a big complex competition environment, and some of the factors that should be considered are the number of competitors, different dynamics of different products, different strategies in the different phases of product life cycles, different marketing goals, etc. In this paper a differential game model is presented to carefully analyze optimal advertising policies over finite planning horizon for two companies. Each company has different brands but similar products. The optimal competitive strategies are given by Nash equilibrium based on their different marketing goals. Numerical computations will be used to get optimal policies and dynamic curves. The numerical algorithms can be use to deal with realistic problems.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">161</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">L. HATVANI</style></author><author><style face="normal" font="default" size="100%">F. TOÓKOS</style></author><author><style face="normal" font="default" size="100%">G. TUSNÁDY</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A MUTATION-SELECTION-RECOMBINATION MODEL IN POPULATION GENETICS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">37G15</style></keyword><keyword><style  face="normal" font="default" size="100%">92D25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/25-DSA-28-11.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">27</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We construct a new continuous time selection-mutation-recombination model for population dynamics, which describes the development of the distribution of the different gametes in the population. We show that cyclic mutation rates can result in stable and unstable limit cycles due to Hopf bifurcation. In addition, we give a qualitative characterization of the whole dynamics in the simplex, which is the phase space of the system. If only selection acts, then Fisher’s Fundamental Law is valid: the mean fitness is a Lyapunov function and every orbit converges to some rest point.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">335</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">B. C. DHAGE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NONLINEAR QUADRATIC FIRST ORDER FUNCTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH PERIODIC BOUNDARY CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/23-DSA-138.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">19</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, an existence theorem for the periodic boundary value problems of first order quadratic functional integro-differential equations is proved via a fixed point theorem in Banach algebras and under some mixed generalized Lipschitz and Carath´eodory conditions. The existence theorems for extremal positive solutions are also proved under certain monotonicity conditions.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">303</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BASAK KARPUZ</style></author><author><style face="normal" font="default" size="100%">ÖZKAN  ÖCALAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OSCILLATION AND NONOSCILLATION OF FIRST-ORDER DYNAMIC EQUATIONS WITH POSITIVE AND NEGATIVE COEFFICIENTS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/26-DSA-154.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this article, we investigate oscillatory nature of all solutions of a class of delay dynamic equations including positive and negative coefficients. Also we give a nonoscillation criterion for this class of delay dynamic equations. While our results reduce to the well-known oscillation criteria for the particular cases of the time scale, they improve recent results on arbitrary time scales. Further, we give some illustrating examples as applications of our results&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">363</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">YIN-LIAN FU</style></author><author><style face="normal" font="default" size="100%">QI-RU WANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OSCILLATION CRITERIA FOR SECOND-ORDER NONLINEAR DAMPED DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/27-DSA-156.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;By employing a class of kernel functions Φ (t, s, l) and a generalized Riccati technique, some new oscillation criteria are established for second-order nonlinear damped differential equations, which extend, improve and unify some related results known in the literature.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">375</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BIYING WANG</style></author><author><style face="normal" font="default" size="100%">ZHITING XU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OSCILLATION OF SECOND ORDER NEUTRAL EMDEN-FOWLER DELAY DYNAMIC EQUATIONS OF MIXED TYPE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/31-DSA-165.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;By means of generalized Riccati transformation and averaging technique, we establish some oscillation criteria for the second-order neutral Emden-Fowler delay dynamic equation of mixed type&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;&amp;nbsp; &amp;nbsp; &amp;nbsp; ( r(t)x&lt;sup&gt;∆&lt;/sup&gt;(t) )&lt;sup&gt;∆ &lt;/sup&gt;+ q&lt;sub&gt;1&lt;/sub&gt;(t) |y( δ(t) )|&lt;sup&gt;α−1&lt;/sup&gt; y( δ(t) ) + q&lt;sub&gt;2&lt;/sub&gt;(t) |y( δ(t) )|&lt;sup&gt;β−1&lt;/sup&gt; y( δ(t) ) = 0,&lt;/p&gt;

&lt;p&gt;on a time scale T. Our results as a special case when T = R improve some well known oscillation criteria for second order neutral Emden-Fowler delay differential equation of mixed type, and when T = N, T = hN, and T = q&lt;sup&gt;No&lt;/sup&gt; , i.e., for neutral delay difference equations, neutral delay difference equations with constant step size, and q-neutral difference equations with variable step size. The results obtained here are essentially new and can be applied to different types of time scales. Some applications and examples are considered to illustrate the main results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">441</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">LIANZHONG LI</style></author><author><style face="normal" font="default" size="100%">FANWEI MENG</style></author><author><style face="normal" font="default" size="100%">ZHAOWEN ZHENG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OSCILLATION RESULTS RELATED TO INTEGRAL AVERAGING TECHNIQUE FOR LINEAR HAMILTONIAN SYSTEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">35A15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/48-DSA-228.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;For linear Hamiltonian systems, even for self-adjoint second order differential systems, we obtain new oscillation results without the assumptions which have been required for related results given before. The main tool used is a generalized Riccati transformation and the standard integral averaging technique.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">725</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">YOU-HUI SU</style></author><author><style face="normal" font="default" size="100%">WAN-TONG LI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">PERIODIC SOLUTION FOR NON-AUTONOMOUS SECOND ORDER HAMILTONIAN SYSTEMS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C25</style></keyword><keyword><style  face="normal" font="default" size="100%">37J45</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A11</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/41-DSA-207.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider the following non-autonomous second order Hamiltonian system on time scales T of the form    u ∆∆(ρ(t)) = ▽H(t, u(t)) ∆-a.e. t ∈ [0, T ]T, u(0) − u(T ) = u ∆(ρ(0)) − u ∆(ρ(T )) = 0. As is well known, it is very difficult to use the Hilger’s integral to consider the existence of periodic solutions of some second order Hamiltonian systems on time scales since it is only concerned with antiderivatives. Therefore, in this paper, we use a new integral on time scales T defined by Rynne (J. Math. Anal. Appl. 328 (2007) 1217–1236), and establish a new existence result for periodic solutions in H1 T (T, R n) space of the above-mentioned second order Hamiltonian system on time scales T by applying variational methods and critical theory. As an application, an example is given to illustrate the result.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">621</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">John R. Graef</style></author><author><style face="normal" font="default" size="100%">TOUFIK MOUSSAOUI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">POSITIVE SOLUTIONS FOR DISCRETE BOUNDARY VALUE PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B16</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/21-DSA-28-10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Existence results for positive solutions are established for a discrete Dirichlet boundary value problem. Various fixed point techniques including the Guo-Krasnosels’kii theorem and Schauder’s fixed point theorem are used. Examples illustrating the results are included.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">265</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ILKAY  KARACA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON POSITIVE SOLUTIONS FOR HIGHER-ORDER BOUNDARY VALUE PROBLEMS WITH IMPULSE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/46-DSA-224.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we consider a higher-order boundary value problem with impulse. We study the existence of at least one positive solution of an eigenvalue problem. Later, we establish the criteria for the existence of at least two positive solutions of a non-eigenvalue problem. Examples are also included to illustrate our results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">687</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">C. Y. CHAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">QUENCHING CRITERIA FOR A DEGENERATE PARABOLIC PROBLEM DUE TO A CONCENTRATED NONLINEAR SOURCE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35B35</style></keyword><keyword><style  face="normal" font="default" size="100%">35K57</style></keyword><keyword><style  face="normal" font="default" size="100%">35K60</style></keyword><keyword><style  face="normal" font="default" size="100%">35K65</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/11-DSA-CY-10-Chan.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">7</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A criterion for the quenching of the solution for a degenerate semilinear parabolic first initial-boundary value problem with a concentrated nonlinear source situated at b is given. The locations of b for global existence of the solution and for the quenching of the solution are given.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">121</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">C. Y. CHAN</style></author><author><style face="normal" font="default" size="100%">T. TREEYAPRASERT</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">QUENCHING FOR A PARABOLIC PROBLEM DUE TO A CONCENTRATED NONLINEAR SOURCE ON A SEMI-INFINITE INTERVAL</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35K57</style></keyword><keyword><style  face="normal" font="default" size="100%">35K60</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/05-DSA-CY-5-ChanTreeyaprasert.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let α, b, and T be positive numbers, D = (0,∞), D¯ = [ 0, ∞ ), and Ω = D × ( 0, T ]. This article studies the first initial-boundary value problem with a concentrated nonlinear source situated at b,&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;u&lt;sub&gt;t&lt;/sub&gt; − u&lt;sub&gt;xx&lt;/sub&gt; = αδ( x − b ) f( u(x, t) )&amp;nbsp; in Ω,&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;u( x, 0 ) = 0 on D¯,&amp;nbsp;&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;u( 0, t ) = 0 and u( x, t ) → 0 as x → ∞&amp;nbsp; for&amp;nbsp; 0 &amp;lt; t ≤ T,&lt;/p&gt;

&lt;p&gt;where δ (x) is the Dirac delta function and f is a given function such that lim&lt;sub&gt;u→c−&lt;/sub&gt; f (u) = ∞ for some positive constant c, and f(u) and its derivatives f´(u) and f''(u) are positive for 0 ≤ u &amp;lt; c. The problem has a unique continuous solution u before sup {u (x, t) : 0 ≤ x &amp;lt; ∞} reaches c&lt;sup&gt;−&lt;/sup&gt;, and u is a strictly increasing function of t in Ω. It is shown that if&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; sup { u (x, t) : 0 ≤ x &amp;lt; ∞ }&lt;/p&gt;

&lt;p&gt;reaches c&lt;sup&gt;−&lt;/sup&gt;, then u attains the value c in a finite time only at the point b. A criterion for u to exist globally and a criterion for u to quench in a finite time are given. It is also shown that there exists a critical position b&lt;sup&gt;∗&lt;/sup&gt; for the nonlinear source to be placed such that for b ≤ b&lt;sup&gt;∗&lt;/sup&gt; , u exists for 0 ≤ t &amp;lt; ∞,&amp;nbsp; and for b &amp;gt; b&lt;sup&gt;∗&lt;/sup&gt; , u quenches in a finite time. This also implies that u does not quench in infinite time. The formula for computing b&lt;sup&gt;∗&lt;/sup&gt; is also derived.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">55</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">C. Y. CHAN</style></author><author><style face="normal" font="default" size="100%">H. T. LIU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">QUENCHING FOR DEGENERATE PARABOLIC PROBLEMS WITH NONLOCAL BOUNDARY CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35K20</style></keyword><keyword><style  face="normal" font="default" size="100%">35K55</style></keyword><keyword><style  face="normal" font="default" size="100%">35K57</style></keyword><keyword><style  face="normal" font="default" size="100%">35K60</style></keyword><keyword><style  face="normal" font="default" size="100%">35K65</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/02-DSA-CY-2-ChanLiu.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let q be a nonnegative real number, and a and T be positive constants. This article studies the following degenerate parabolic problem: x qut − uxx = G(u) in (0, a) × (0, T], where G is a nonnegative function in the form of either f(u(x, t)), or Ra 0 h(x, t) f(u(x, t))dx for some positive, bounded and continuous function h with f &amp;gt; 0, f 0&amp;gt; 0, f 00≥ 0, and limu→1− f(u) = ∞. It is subject to the initial condition, u(x, 0) = 0 on [0, a], and the boundary conditions, u(0, t) = Za 0 M(x)|u (x, t)| p dx, u (a, t) = Za 0 N (x)|u (x, t)| r dx, t &amp;gt; 0, where p and r are constants greater than or equal to 1, and M and N are given nonnegative functions. Existence, uniqueness and criteria for quenching and non-quenching are studied.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">17</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JUN LIU</style></author><author><style face="normal" font="default" size="100%">XINZHI LIU</style></author><author><style face="normal" font="default" size="100%">WEI-CHAU XIE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ROBUST STABILIZATION OF STOCHASTIC SWITCHED DELAY SYSTEMS VIA STATE-DEPENDENT SWITCHING RULE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34F05</style></keyword><keyword><style  face="normal" font="default" size="100%">34K50</style></keyword><keyword><style  face="normal" font="default" size="100%">60H99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/18-DSA-28-07.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">27</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper considers the robust stabilization of uncertain stochastic switched systems with constant time-delay. While most of the results on stability analysis of switched systems in literature assume all subsystems are stable, the results of this paper can deal with stochastic switched systems consisting of unstable subsystems. Assuming there exists a Hurwitz linear convex combination for the original system, it is shown that a state-dependent switching rule can be found to stabilize the stochastically perturbed system with both uncertainties and time-delay, provided that the perturbation, uncertainties, and time-delay are sufficiently small. An effort was made to give an explicit stability upper bound for the time-delay. The results are also extended to nonlinear systems. Numerical examples are presented to demonstrate the results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">213</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ANNE KANDLER</style></author><author><style face="normal" font="default" size="100%">MATTHIAS RICHTER</style></author><author><style face="normal" font="default" size="100%">JÜRGEN VOM SCHEIDT</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SECOND ORDER MOMENTS OF SOLUTIONS OF PARABOLIC INITIAL BOUNDARY VALUE PROBLEMS WITH ε-CORRELATED RANDOM PARAMETERS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">60G60</style></keyword><keyword><style  face="normal" font="default" size="100%">60H35</style></keyword><keyword><style  face="normal" font="default" size="100%">65N30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/13-DSA-27-05.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Due to the random character of input data of a great variety of technical and economical procedures it seems to be appropriate to model these procedures by stochastic initial boundary value problems (IBVP). This paper deals with IBVP for parabolic partial differential equations where a Neumann boundary condition is assumed to be a random field with a given probability distribution. We assume, that this random field possesses smooth paths and that it is homogeneous and short-range correlated with a small correlation length ε &amp;gt; 0. The main interest lies in the calculation of the moment functions of the solution of the considered problem, which depend on the chosen characteristics of the random influence. Based on the idea of an appropriate FEM discretisation we present several approximation procedures for the computation of the variance and correlation function of the discretised solution. Considering a numerical example the resulting variance functions of the introduced methods are compared with the results of a Monte Carlo simulation.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">143</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JÓZEF BANAS</style></author><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author><author><style face="normal" font="default" size="100%">KISHIN SADARANGANI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON SOLUTIONS OF A QUADRATIC HAMMERSTEIN INTEGRAL EQUATION ON AN UNBOUNDED INTERVAL</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">45G10</style></keyword><keyword><style  face="normal" font="default" size="100%">47H09</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/20-DSA-28-09.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we examine the solvability of a nonlinear quadratic Hammerstein integral equation. This equation is considered in the Banach space of real functions which are defined, bounded and continuous on the real half-line. Using the idea of measures of noncompactness with the classical Schauder fixed point theorem we show that the equation has solutions which vanish at infinity.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">251</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JINHAI CHEN</style></author><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOLVABILITY ANALYSIS OF PERIODIC SOLUTIONS FOR nTH ORDER DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">34L16</style></keyword><keyword><style  face="normal" font="default" size="100%">65L05</style></keyword><keyword><style  face="normal" font="default" size="100%">65L10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/17-DSA-28-06.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">7</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, by using an initial value problem method and a global inverse function theorem, we give some existence and uniqueness results of periodic solution for a class of nth-order nonlinear ordinary differential equations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">205</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">LESZEK OLSZOWY</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOLVABILITY OF SOME FUNCTIONAL INTEGRAL EQUATION</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">45N05</style></keyword><keyword><style  face="normal" font="default" size="100%">47B38</style></keyword><keyword><style  face="normal" font="default" size="100%">47H09</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/44-DSA-218.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we present results on the existence and asymptotic behaviour of solutions of a functional integral equation. Considering the equation in Banach space and proving a new fixed point theorem we establish existence theorems which generalize several ones obtained earlier by other authors. The applicability of the results is illustrated by an example.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">667</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">KIL-WOUNG JUN</style></author><author><style face="normal" font="default" size="100%">YANG-HI LEE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE STABILITY OF A CAUCHY-JENSEN FUNCTIONAL EQUATION II</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39B52</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/29-DSA-159.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we prove the generalized Hyers-Ulam stability of a Cauchy-Jensen functional equation 2f(x + y, z + w 2 ) = f(x, z) + f(x, w) + f(y, z) + f(y, w) in the spirit of P. Gâvruta.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">407</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">YONG-SOO JUNG</style></author><author><style face="normal" font="default" size="100%">KYOO-HONG PARK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE STABILITY OF HIGHER GENERALIZED RING DERIVATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39B52</style></keyword><keyword><style  face="normal" font="default" size="100%">39B72</style></keyword><keyword><style  face="normal" font="default" size="100%">39B82</style></keyword><keyword><style  face="normal" font="default" size="100%">46H99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/24-DSA-150.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we investigate the generalized Hyers-Ulam-Rassias stability and the Bourgin-type superstability of a functional inequality corresponding to the following functional equation: fn(xy) = Xn i=0 fn−i(x)gi(y)&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">323</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SALIM A. MESSAOUDI</style></author><author><style face="normal" font="default" size="100%">MUHAMMAD I. MUSTAFA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A STABILITY RESULT IN A MEMORY-TYPE TIMOSHENKO SYSTEM</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35B37</style></keyword><keyword><style  face="normal" font="default" size="100%">35L55</style></keyword><keyword><style  face="normal" font="default" size="100%">74D05</style></keyword><keyword><style  face="normal" font="default" size="100%">93D15</style></keyword><keyword><style  face="normal" font="default" size="100%">93D20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/32-DSA-170.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we consider the following Timoshenko system ϕtt − (ϕx + ψ)x = 0, (0, 1) × IR+ ψtt − ψxx + ϕx + ψ + Zt 0 g(t − τ)ψxx(τ)dτ = 0, (0, 1) × IR+ with Dirichlet boundary conditions where g is a positive nonincreasing function. We establish a generalized stability result for this system.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">457</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ANNA GÓRALCZYK</style></author><author><style face="normal" font="default" size="100%">JERZY MOTYL</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STRATONOVICH STOCHASTIC INCLUSION</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">49J53</style></keyword><keyword><style  face="normal" font="default" size="100%">60H20</style></keyword><keyword><style  face="normal" font="default" size="100%">93E03</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/16-DSA-28-05.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The purpose of the paper is to investigate the existence of strong solutions for&lt;br /&gt;
the Stratonovich type stochastic inclusion with maximal monotone and upper separated set-valued&lt;br /&gt;
functions.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">191</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">R. HILSCHER</style></author><author><style face="normal" font="default" size="100%">P. ZEMANEK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">TRIGONOMETRIC AND HYPERBOLIC SYSTEMS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C99</style></keyword><keyword><style  face="normal" font="default" size="100%">39A12</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/34-DSA-180.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">23</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we discuss trigonometric and hyperbolic systems on time scales. These systems generalize and unify their corresponding continuous-time and discrete-time analogies, namely the systems known in the literature as trigonometric and hyperbolic linear Hamiltonian systems and discrete symplectic systems. We provide time scale matrix definitions of the usual trigonometric and hyperbolic functions and show that many identities known from the basic calculus extend to this general setting, including the time scale differentiation of these functions.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">483</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ARIE LEIZAROWITZ</style></author><author><style face="normal" font="default" size="100%">BENJAMIN LENGER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ADDITIVE DECOMPOSITION OF MATRICES AND OPTIMIZATION PROBLEMS ON INFINITE TIME INTERVALS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-283-302.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We discuss control systems over finite and countable state spaces defined on an infinite time horizon, where, typically, all the associated costs become unbounded as the time grows indefinitely. We consider the limit behavior, as n → ∞, of the expression Pn−1 i=0 v(zi , zi+1) for programs {zi}∞ i=0 in a finite state space X = {xi} N i=1, where v(xi , xj ) is the transition cost from state xi to state xj . To construct optimal programs we will establish and employ an additive decomposition formula which is of the form V = µJ + pηT − ηp T + Θ. In this expression µ is a scalar, J is a matrix that satisfies Jij = 1 for every 1 ≤ i, j ≤ N, p and η are N-dimensional column vectors such that ηi = 1 for all 1 ≤ i ≤ N, and Θ is a matrix satisfying min1≤j≤N Θij = 0 for every 1 ≤ i ≤ N. We will show how to compute µ, p and Θ in time of order O(N5 ). Also, we will discuss infinite horizon optimization problems for certain non-autonomous control systems.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">283</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">YEOL-JE CHO</style></author><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author><author><style face="normal" font="default" size="100%">SVATOSLAV STANEK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ANTIPODAL FIXED POINT THEORY FOR VOLTERRA MAPS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-325-330.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">6</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;New antipodal fixed point theorems for compact Kakutani maps between Frechet spaces are presented.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">325</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RAHMAT  KHAN</style></author><author><style face="normal" font="default" size="100%">JUAN NIETO</style></author><author><style face="normal" font="default" size="100%">ANGELA TORRES</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">APPROXIMATION AND RAPID CONVERGENCE OF SOLUTIONS FOR PERIODIC NONLINEAR PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A45</style></keyword><keyword><style  face="normal" font="default" size="100%">34C25</style></keyword><keyword><style  face="normal" font="default" size="100%">92C50</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-121-138.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study existence and approximation of solutions of some second order nonlinear periodic boundary value problem of the type&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;&amp;nbsp;−x''(t) = f(t, x, x' ),&amp;nbsp; &amp;nbsp; &amp;nbsp;&amp;nbsp;t ∈ [0, T],&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;x(0) = x(T),&amp;nbsp; x'(0) = x'(T),&lt;/p&gt;

&lt;p&gt;in the presence of lower and upper solutions. We develop the upper and lower solutions method and the quasilinearization technique for the existence and approximation of solutions. We apply our theoretical results to a medical problem.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">121</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SHIH-SEN CHANG</style></author><author><style face="normal" font="default" size="100%">YEOL-JE CHO</style></author><author><style face="normal" font="default" size="100%">JONG-KYU KIM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">APPROXIMATION METHODS OF SOLUTIONS FOR EQUILIBRIUM PROBLEM IN HILBERT SPACES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H09</style></keyword><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-503-514.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The purpose of this paper is, by using viscosity approximation methods, to find a common element of the set of solutions of an equilibrium problem and the set of fixed point of a nonexpansive mappings in a Hilbert space and to prove, under suitable conditions, some strong convergence theorems for approximating a solution of the problem under consideration.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">503</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">HÜSEYIN  BEREKETOGLU</style></author><author><style face="normal" font="default" size="100%">FATMA KARAKOÇ</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ASYMPTOTIC CONSTANCY FOR IMPULSIVE DELAY DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K06</style></keyword><keyword><style  face="normal" font="default" size="100%">34K45</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-071-084.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Sufficient conditions for the asymptotic constancy of the solutions of impulsive delay differential system ( x 0 (t) = A(t)[x(t − σ) − x(t − τ )] + f(t), t ≥ t0, t 6= ti , ∆x(ti) = Bix(ti) + Di , i = 1, 2, . . . , are obtained. Moreover, as t → ∞, the limits of the solutions of the impulsive delay differential system with Bi = 0 are computed in terms of the initial function and a special matrix solution of the corresponding adjoint system.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">71</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RUYUN MA</style></author><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ASYMPTOTIC NONUNIFORM NONRESONANCE CONDITIONS FOR A NONLINEAR DISCRETE BOUNDARY VALUE PROBLEM</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-271-282.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let T := {a+1, . . . , b+1}. We study the solvability of nonlinear discrete two-point boundary value problem ( ∆2u(t − 1) + g(t, u(t)) = h(t), t ∈ T, u(a) = u(b + 2) = 0 where h : T → R, g : T × R → R satisfies α(t) ≤ lim inf |x|→∞ x −1 g(t, x) ≤ lim sup |x|→∞ x −1 g(t, x) ≤ β(t) uniformly on T, and α and β satisfy some nonresonance conditions of nonuniform type with respect to two consecutive eigenvalues of the associated linear problem. The proof is based on the LeraySchauder continuation theorem.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">271</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SORAYA LABIDI</style></author><author><style face="normal" font="default" size="100%">NASSER-EDDINE TATAR</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">BLOW-UP FOR THE EULER-BERNOULLI BEAM PROBLEM WITH A FRACTIONAL BOUNDARY DISSIPATION</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">35B37</style></keyword><keyword><style  face="normal" font="default" size="100%">35B40</style></keyword><keyword><style  face="normal" font="default" size="100%">35B45</style></keyword><keyword><style  face="normal" font="default" size="100%">45K05</style></keyword><keyword><style  face="normal" font="default" size="100%">93B52</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-109-120.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider a beam problem with a polynomial source and a boundary damping of order between 0 and 1. Sufficient conditions on the initial data are established to have blow up of solutions in finite time.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">109</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">K. BALACHANDRAN</style></author><author><style face="normal" font="default" size="100%">J.-H. KIM</style></author><author><style face="normal" font="default" size="100%">S.KARTHIKEYAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">COMPLETE CONTROLLABILITY OF STOCHASTIC INTEGRODIFFERENTIAL SYSTEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">93B05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-043-052.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper sufficient conditions for the complete controllability of stochastic semilinear integrodifferential system in finite dimensional spaces are established. The results are obtained by using the Banach fixed point theorem. An example is provided to illustrate the technique.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">43</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">L. MANCA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">DIFFERENTIABLE PERTURBATIONS OF ORNSTEIN-UHLENBECK OPERATORS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47A55</style></keyword><keyword><style  face="normal" font="default" size="100%">47B38</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-435-444.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We prove an extension theorem for a small perturbation of the Ornstein-Uhlenbeck operator (L, D(L)) in the space of all uniformly continuous and bounded functions f : H → R, where H is a separable Hilbert space. We consider a perturbation of the form N&lt;sub&gt;0&lt;/sub&gt;ϕ = Lϕ + (Dϕ, F) where F : H → H is bounded and Fréchet differentiable with uniformly continuous and bounded differential. Hence, we prove that N&lt;sub&gt;0&lt;/sub&gt; is essentially m-dissipative and its closure in C&lt;sub&gt;b&lt;/sub&gt;(H) coincides with the infinitesimal generator of a diffusion semigroup associated to a stochastic differential equation in H.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">435</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MOHAMED  EL-GEBEILY</style></author><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE AND QUASILINEARIZATION FOR A CLASS OF NONLINEAR ELLIPTIC SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">41A65</style></keyword><keyword><style  face="normal" font="default" size="100%">47J05</style></keyword><keyword><style  face="normal" font="default" size="100%">47J25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-445-458.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we discuss some existence results and the application of quasilinearization methods to the solution of second order nonlinear self adjoint elliptic partial differential equation in R&lt;sup&gt;n&lt;/sup&gt; with Dirichlet boundary conditions. Under fairly general assumptions on the data of the problem we show the existence of a solution that can be obtained as the limit of a quadratically convergent nondecreasing sequence of approximate solutions. If the assumptions are strengthened, we show that the solution can be quadratically bracketed between two monotone sequences of approximate solutions of certain related linear equations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">445</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">YU TIAN</style></author><author><style face="normal" font="default" size="100%">DAQING JIANG</style></author><author><style face="normal" font="default" size="100%">WEIGAO GE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF POSITIVE SOLUTIONS FOR PERIODIC BOUNDARY VALUE PROBLEMS WITH IMPULSE EFFECTS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">34b18</style></keyword><keyword><style  face="normal" font="default" size="100%">34B37</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-167-184.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper is devoted to study the existence of multiple positive solutions for the second order periodic boundary value problems with impulse effects. By imposing different conditions on nonlinearity, we establish various of existence results. Besides, some results generalize Jiang [5] for ordinary differential equations. In particular, nonlinearity involving the first derivative of x is considered.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">167</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ISMAIL YASLAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF SOLUTIONS FOR BOUNDARY VALUE PROBLEMS ON INFINITE INTERVALS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">34B40</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-653-662.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, the Schauder fixed point theorem is used to investigate the existence of solutions of the boundary value problems (BVP) for second-order nonlinear differential equations on infinite intervals.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">653</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ABDELHAMID BENMEZAÏ</style></author><author><style face="normal" font="default" size="100%">SMAIL DJEBALI</style></author><author><style face="normal" font="default" size="100%">TOUFIK MOUSSAOUI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE RESULTS FOR ONE-DIMENSIONAL DIRICHLET φ-LAPLACIAN BVPS: A FIXED POINT APPROACH</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">34b18</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-149-166.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The aim of this paper is to present new existence results for φ-Laplacian Dirichlet boundary value problems set on bounded intervals of the real line. The fixed point theory approach and continuation methods are used throughout. Generalizations of some previous results regarding second-order differential equations are obtained.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">149</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">WEIMIN HU</style></author><author><style face="normal" font="default" size="100%">DAQING JIANG</style></author><author><style face="normal" font="default" size="100%">GEXIN LUO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE THEORY FOR SINGLE AND MULTIPLE SOLUTIONS TO SINGULAR DISCRETE BOUNDARY VALUE PROBLEMS OF SECOND-ORDER DIFFERENTIAL SYSTEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-221-234.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we establish the existence of single and multiple solutions to the singular discrete boundary value problem    ∆2x(i − 1) + q1(i)f1(i, x(i), y(i)) = 0, i ∈ {1, 2, . . . , T}, ∆2y(i − 1) + q2(i)f2(i, x(i), y(i)) = 0, x(0) = x(T + 1) = y(0) = y(T + 1) = 0, where nonlinear term fk(i, x, y) may be singular at (x, y) = (0, 0), k = 1, 2.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">221</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">A. M. SAMOILENKO</style></author><author><style face="normal" font="default" size="100%">N. I. MAHMUDOV</style></author><author><style face="normal" font="default" size="100%">A. N. STANZHITSKII</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE, UNIQUENESS, AND CONTROLLABILITY RESULTS FOR NEUTRAL FSDES IN HILBERT SPACES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">93B05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-053-070.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We establish results concerning the global existence, uniqueness, and controllability of mild solutions for a neutral functional stochastic differential equations with variable delay in a real separable Hilbert space. The results are obtained by imposing a so-called Carathe´odory condition on the nonlinearities, which is weaker than the classical Lipschitz condition. Examples illustrating the applicability of the general theory are also provided.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">53</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">TADEUSZ JANKOWSKI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">FRACTIONAL DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A12</style></keyword><keyword><style  face="normal" font="default" size="100%">34A40</style></keyword><keyword><style  face="normal" font="default" size="100%">34K05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-677-684.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">7</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper deals with initial problems for fractional differential equations with deviating arguments. Sufficient conditions are formulated under which such problems have unique or extremal solutions. Corresponding inequalities for such problems are also discussed.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">677</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">E.O. AYOOLA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">FURTHER RESULTS ON THE EXISTENCE OF CONTINUOUS SELECTIONS OF SOLUTION SETS OF QUANTUM STOCHASTIC DIFFERENTIAL INCLUSIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword><keyword><style  face="normal" font="default" size="100%">81S25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-609-624.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We prove that the map that associates to the initial value the set of solutions to the Lipschitzian Quantum Stochastic Differential Inclusion (QSDI) admits a selection which is continuous from the locally convex space of stochastic processes to the space of adapted and weakly absolutely continuous solutions. As a corollary, the reachable set multifunction admits a continuous selection. In the framework of the Hudson-Parthasarathy formulation of quantum stochastic calculus, these results are achieved subject to some compactness conditions on the set of initial values and on some coefficients of the inclusion.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">609</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JUAN J. NIETO</style></author><author><style face="normal" font="default" size="100%">ROSANA RODRIGUEZ-LOPEZ</style></author><author><style face="normal" font="default" size="100%">D. N. GEORGIOU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">FUZZY DIFFERENTIAL SYSTEMS UNDER GENERALIZED METRIC SPACES APPROACH</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26E50</style></keyword><keyword><style  face="normal" font="default" size="100%">34A12</style></keyword><keyword><style  face="normal" font="default" size="100%">34A34</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-001-024.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">24</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study the existence and uniqueness of solution for fuzzy differential systems under the point of view of generalized metric spaces. The results obtained are applied to study the solvability of first-order fuzzy linear systems, as well as higher-order fuzzy differential equations and systems.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">1</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BASHIR AHMAD</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">GENERALIZED QUASILINEARIZATION FOR NONLINEAR IMPULSIVE THREE-POINT BOUNDARY VALUE PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A37</style></keyword><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-185-200.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We apply the generalized quasilinearization technique to obtain a monotone sequence of iterates converging monotonically and quadratically to a unique solution of an impulsive threepoint general nonlinear second order boundary value problem. The nth order (n ≥ 2) convergence of the sequence of iterates has also been accomplished.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">185</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">UMUT OZKAN</style></author><author><style face="normal" font="default" size="100%">HUSEYIN YILDIRIM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">HARDY-KNOPP-TYPE INEQUALITIES ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26D15</style></keyword><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-477-486.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper deals with a time scale version of the Hardy-Knopp-Type and the twodimensional Hardy-Knopp-type inequalities. Moreover, Hardy inequality for several functions is presented on time scales.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">477</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ZHAOWEN ZHENG</style></author><author><style face="normal" font="default" size="100%">SIMING ZHU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">HARTMAN TYPE OSCILLATION CRITERIA FOR LINEAR MATRIX HAMILTONIAN SYSTEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A30</style></keyword><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-085-096.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, some new oscillation criteria for linear matrix Hamiltonian systems are established, which involves the maximum eigenvalue of the coefficients. These results improve and generalize some known oscillation criteria due to G. J. Butler, L. H. Erbe and A. B. Mingarelli [1], N. Parhi and P. Praharaj [2] for self-adjoint second order matrix differential systems, and Yang et. al. [4] for linear matrix Hamiltonian systems.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">85</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">M. I. GIL’</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">L2  -STABILITY OF VECTOR EQUATIONS WITH NONLINEAR CAUSAL MAPPINGS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K20</style></keyword><keyword><style  face="normal" font="default" size="100%">34K99</style></keyword><keyword><style  face="normal" font="default" size="100%">93D05</style></keyword><keyword><style  face="normal" font="default" size="100%">93D25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-201-220.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">19</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Nonlinear vector equations with causal mappings are considered. These equations include differential, difference, differential-delay, integro-differential and other traditional equations. Estimates for the L&lt;sup&gt;2&lt;/sup&gt; -norm of solutions are established. The obtained estimates give us explicit conditions for the L&lt;sup&gt;2&lt;/sup&gt; -stability, absolute stability and input-to-state stability of the considered equations as well as bounds for the regions of attraction of stationary states. The suggested approach enables us to consider various classes of equations from the unified point of view.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">201</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JAUME LLIBRE</style></author><author><style face="normal" font="default" size="100%">JIANG YU</style></author><author><style face="normal" font="default" size="100%">XIANG ZHANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">LIMIT CYCLES COMING FROM THE PERTURBATION OF 2-DIMENSIONAL CENTERS OF VECTOR FIELDS IN R 3</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">37D45</style></keyword><keyword><style  face="normal" font="default" size="100%">37G15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-625-636.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we study the limit cycles of polynomial vector fields in R&lt;sup&gt;3&lt;/sup&gt; which bifurcates from three different kinds of two dimensional centers (non-degenerate and degenerate). The study is down using the averaging theory.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">625</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">H.T. BANKS</style></author><author><style face="normal" font="default" size="100%">NEGASH G. MEDHIN</style></author><author><style face="normal" font="default" size="100%">GABRIELLA  PINTER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MODELING OF VISCOELASTIC SHEAR: A NONLINEAR STICK-SLIP FORMULATION</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-383-406.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">23</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We present a class of nonlinear dynamic viscoelastic models for materials subjected to shear stress. The model equations are based on a continuum variation of a reptation model in which chemically cross-linked (CC) systems of molecules act as constraint boxes per unit volume for physically constrained (PC) systems of molecules. Results from validating the model with dynamic shear experiments are given and a stability analysis for the corresponding linearized systems is discussed.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">383</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MARIELLA CECCHI</style></author><author><style face="normal" font="default" size="100%">ZUZANA DOSLA</style></author><author><style face="normal" font="default" size="100%">MAURO MARINI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MONOTONE SOLUTIONS OF TWO-DIMENSIONAL NONLINEAR FUNCTIONAL DIFFERENTIAL SYSTEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">34C15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-595-608.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The existence of nonoscillatory solutions with different asymptotic properties for a two-dimensional nonlinear functional differential system is studied. Some discrepancies in the coexistence of nonoscillatory solutions between the general nonlinear system and the Emden-Fowler system or the half-linear equation are pointed out. The roles of deviating arguments are also discussed.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">595</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MOHAMED DARWISH</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON MONOTONIC SOLUTIONS OF A SINGULAR QUADRATIC INTEGRAL EQUATION WITH SUPREMUM</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">45G10</style></keyword><keyword><style  face="normal" font="default" size="100%">45M99</style></keyword><keyword><style  face="normal" font="default" size="100%">47H09</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-539-550.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We prove an existence theorem for a singular quadratic integral equation with supremum. The quadratic integral equation studied below contains as a special case numerous integral equations encountered in the theory of radiative transfer and in the kinetic theory of gases. We show that the singular quadratic integral equations with supremum has a monotonic solution in C[0, 1]. The concept of measure of noncompactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">539</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">M. FILIPPAKIS</style></author><author><style face="normal" font="default" size="100%">N.S. PAPAGEORGIOU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MULTIPLE NONTRIVIAL SOLUTIONS FOR SEMILINEAR ELLIPTIC NEUMANN PROBLEMS WITH INDEFINITE LINEAR PART</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35J20 58E05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-371-382.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider a semilinear Neumann problem with indefinite linear part and a nonsmooth potential (hemivariational inequality).Using a nonsmooth variant of the reduction technique, we prove a multiplicity theorem for problems with subquadratic potential.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">371</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ILKAY   KARACA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MULTIPLE POSITIVE SOLUTIONS FOR DYNAMIC m-POINT BOUNDARY VALUE PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-025-042.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we consider a second order m-point boundary value problem for dynamic equations on time scales. First, we establish criteria for the existence of one or more than one positive solution of a non-eigenvalue problem. Second, we consider the existence and multiplicity of positive solutions for an eigenvalue problem. We shall also obtain criteria which lead to nonexistence of positive solutions. In both problems, we will use fixed point theorems for operators on a Banach space.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">25</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ANETA SIKORSKA-NOWAK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NONLINEAR INTEGRAL EQUATIONS IN BANACH SPACES AND HENSTOCK-KURZWEIL-PETTIS INTEGRALS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">28B05</style></keyword><keyword><style  face="normal" font="default" size="100%">34G20</style></keyword><keyword><style  face="normal" font="default" size="100%">45D05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-097-108.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We prove an existence theorem for the nonlinear integral equation : x(t) = f(t) + Zα 0 k1(t, s)x(s)ds + Zα 0 k2(t, s)g(s, x(s))ds, t ∈ Iα = [0, α], α ∈ R+, with the Henstock-Kurzweil-Pettis integrals. This integral equation can be considered as a nonlinear Fredholm equation expressed as a perturbed linear equation. The assumptions about the function g are really-weak: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function g satisfies some conditions expressed in terms of the measure of weak noncompactness.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">97</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ALEXANDER  ZASLAVSKI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NONOCCURRENCE OF THE LAVRENTIEV PHENOMENON FOR MANY INFINITE DIMENSIONAL LINEAR CONTROL PROBLEMS WITH NONCONVEX INTEGRANDS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">49J27</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-407-434.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">28</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we establish nonoccurrence of gap for two large classes of infinitedimensional linear control systems in a Hilbert space with nonconvex integrands. These classes are identified with the corresponding complete metric spaces of integrands which satisfy a growth condition common in the literature. For most elements of the first space of integrands (in the sense of Baire category) we establish the existence of a minimizing sequence of trajectory-control pairs with bounded controls. We also establish that for most elements of the second space (in the sense of Baire category) the infimum on the full admissible class of trajectory-control pairs is equal to the infimum on a subclass of trajectory-control pairs whose controls are bounded by a certain constant.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">407</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MEHMET SARIKAYA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A NOTE ON GRUSS TYPE INEQUALITIES ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26D15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-663-666.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">4</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The purpose of this paper is to investigate some Gr¨uss type inequalities on time scales. Our results unify some continuous inequalities and their corresponding discrete analogues. We also apply our results to the quantum calculus case.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">663</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">N. U. AHMED</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OPTIMAL CHOICE OF NONLINEAR OUTPUT FEEDBACK CONTROL LAW FOR A CLASS OF UNCERTAIN PARABOLIC SYSTEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47A62</style></keyword><keyword><style  face="normal" font="default" size="100%">49J20</style></keyword><keyword><style  face="normal" font="default" size="100%">49J24</style></keyword><keyword><style  face="normal" font="default" size="100%">49N35</style></keyword><keyword><style  face="normal" font="default" size="100%">65N21</style></keyword><keyword><style  face="normal" font="default" size="100%">93B52</style></keyword><keyword><style  face="normal" font="default" size="100%">93C20</style></keyword><keyword><style  face="normal" font="default" size="100%">93C25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-571-582.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we consider optimal output feedback boundary control problems for a class of semilinear uncertain parabolic systems. The uncertain initial boundary value problem is converted into an equivalent Cauchy problem described by a differential inclusion in appropriate Banach spaces. We follow game-theoretic formalism and prove existence of saddle points giving optimal strategies. This is an extension of a recent result of the author from linear to a class of nonlinear feedback operators. The paper is concluded with a brief description of open problems and future directions.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">571</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Z. G. FENG</style></author><author><style face="normal" font="default" size="100%">K. L. TEO</style></author><author><style face="normal" font="default" size="100%">V. REHBOCK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OPTIMAL SENSOR SCHEDULING IN CONTINUOUS TIME</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-331-350.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we consider an optimal sensor scheduling problem in continuous time. This problem aims to find an optimal sensor schedule such that the corresponding estimation error is minimized. It is formulated as a deterministic optimal control problem involving both discrete and continuous valued controls. A computational method is developed for solving this deterministic optimal control problem based on a branch and bound method in conjunction with a gradient-based method. The branch and bound method is used to determine the optimal switching sequence of sensors, where a sequence of lower bound dynamic systems is introduced so as to provide effective lower bounds for the construction of the branching rules. For a given switching sequence, determining the respective optimal switching time is a continuous-valued optimal control problem and can be solved by gradient-based method with appropriate gradient formulae. This computational method is very efficient, as demonstrated by the numerical examples.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">331</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Z.G. FENG</style></author><author><style face="normal" font="default" size="100%">K.L. TEO</style></author><author><style face="normal" font="default" size="100%">V. REHBOCK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OPTIMAL SENSOR SCHEDULING IN CONTINUOUS TIME</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-331-350.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we consider an optimal sensor scheduling problem in continuous time. This problem aims to find an optimal sensor schedule such that the corresponding estimation error is minimized. It is formulated as a deterministic optimal control problem involving both discrete and continuous valued controls. A computational method is developed for solving this deterministic optimal control problem based on a branch and bound method in conjunction with a gradient-based method. The branch and bound method is used to determine the optimal switching sequence of sensors, where a sequence of lower bound dynamic systems is introduced so as to provide effective lower bounds for the construction of the branching rules. For a given switching sequence, determining the respective optimal switching time is a continuous-valued optimal control problem and can be solved by gradient-based method with appropriate gradient formulae. This computational method is very efficient, as demonstrated by the numerical examples.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">331</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DEVRIM ÇAKMAK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OSCILLATION FOR SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH DAMPING</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">34C15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-139-148.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Some new oscillation criteria are given for second order nonlinear differential equations with damping of the form&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; ( r(t) x' )'+ p(t) x'+ q (t) f(x) = 0.&amp;nbsp;&lt;/p&gt;

&lt;p&gt;Our results are to develop oscillation criteria without any restriction on the signs of p (t) and q (t). These results generalize and extend some earlier results of Abdullah [1] and Zheng and Liu [12].&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">139</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Ö. ÖCALAN</style></author><author><style face="normal" font="default" size="100%">M.K. YILDIZ</style></author><author><style face="normal" font="default" size="100%">B. KARPUZ</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE OSCILLATION OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATION WITH POSITIVE AND NEGATIVE COEFFICIENTS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">34K40</style></keyword><keyword><style  face="normal" font="default" size="100%">34K99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-667-676.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper is focused on the following nonlinear neutral differential equation with positive and negative coefficients&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;[ x(t) − R(t) f( x(t − r)) ]′ + P(t) g(x(t − τ)) − Q(t )g( x(t − σ)) = 0,&lt;/p&gt;

&lt;p&gt;where R(t), P(t), Q(t) ∈ C ([t&lt;sub&gt;0&lt;/sub&gt;, ∞), R&lt;sup&gt;+&lt;/sup&gt;),&amp;nbsp; r &amp;gt; 0,&amp;nbsp; τ ≥ 0,&amp;nbsp; σ ≥ 0. For this equation, oscillation criteria are established.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">667</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">HAO HUANG</style></author><author><style face="normal" font="default" size="100%">QI-RU WANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OSCILLATION OF SECOND-ORDER NONLINEAR DYNAMIC EQUATIONS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-551-570.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;By using the functions of the form H(t, s) and a generalized Riccati technique, we establish new Kamenev-type and interval oscillation criteria for second-order nonlinear dynamic equations on time scales of the form&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;( p(t)x&lt;sup&gt;∆&lt;/sup&gt;(t) )&lt;sup&gt;∆&lt;/sup&gt; + f( t, x(σ(t)) ) = 0.&lt;/p&gt;

&lt;p&gt;The obtained interval oscillation criteria can be applied to equations with forcing term. Two examples are included to show the significance of the results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">551</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">E.H.  DADS</style></author><author><style face="normal" font="default" size="100%">P. CIEUTAT</style></author><author><style face="normal" font="default" size="100%">L. LHACHIMI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">POSITIVE ALMOST AUTOMORPHIC SOLUTIONS FOR SOME NONLINEAR INFINITE DELAY INTEGRAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">42A75</style></keyword><keyword><style  face="normal" font="default" size="100%">44A35</style></keyword><keyword><style  face="normal" font="default" size="100%">45G10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-515-538.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">24</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We state sufficient conditions for the existence of positive bounded, almost automorphic or almost periodic solutions of the following nonlinear infinite delay integral equation: x(t) = Zt −∞ a(t, t − s)f(s, x(s)) ds. Then we apply these results to a finite delay integral equation when the delay is time-dependent and for a delay differential equation.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">515</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">E.O. AYOOLA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">QUANTUM STOCHASTIC DIFFERENTIAL INCLUSIONS SATISFYING A GENERAL LIPSCHITZ CONDITION</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword><keyword><style  face="normal" font="default" size="100%">81S25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-487-502.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We establish further results concerning the existence and non-uniqueness of solutions of quantum stochastic differential inclusions in the framework of Hudson and Parthasarathy formulation of quantum stochastic calculus. Our results are established by considering a general Lipschitz condition on the coefficients of the inclusion. We present examples of continuous multivalued maps satisfying the general Lipschitz condition in the sense of this paper.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">487</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">PABLO FIGUEROA</style></author><author><style face="normal" font="default" size="100%">MANUEL PINTO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">RICCATI EQUATIONS AND NONOSCILLATORY SOLUTIONS OF THIRD ORDER DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34E05</style></keyword><keyword><style  face="normal" font="default" size="100%">34E10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-459-476.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study the existence of special solutions of second order Riccati type equations. We apply these results to third order linear differential equations with almost constant coefficients. We give new sufficient conditions to know the asymptotic behavior of the logarithmic derivative of a solution y. We recover Poincar´e and Perron’s results and other asymptotic formulae. Furthermore, we obtain some weaker versions of Levinson and Hartman-Wintner type Theorems.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">459</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JIAN-PING SUN</style></author><author><style face="normal" font="default" size="100%">WAN-TONG LI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOLUTIONS AND POSITIVE SOLUTIONS TO SEMIPOSITONE DIRICHLET BVPS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-303-312.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we are concerned with the following Dirichlet boundary value problem on a time scale T ( −u ∆∆(t) = g(t, u(t)), t ∈ [0, T]T, u(0) = 0 = u(σ 2 (T)), where g : [0, T]T×[−σ(T)σ 2 (T)M, +∞) → [−M, +∞) is continuous and M &amp;gt; 0 is a constant, which implies that this problem is semipositone. For an arbitrary positive integer n, some existence results for n solutions and/or positive solutions are established by using the well-known Guo-Krasnosel’skii fixed point theorem. Our conditions imposed on g are local. An example is also included to illustrate the importance of the results obtained.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">303</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JOZEF  BANAS</style></author><author><style face="normal" font="default" size="100%">LESZEK OLSZOWY</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON SOLUTIONS OF A QUADRATIC URYSOHN INTEGRAL EQUATION ON AN UNBOUNDED INTERVAL</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">45G10</style></keyword><keyword><style  face="normal" font="default" size="100%">47H30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-255-270.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We investigate the existence of solutions of a quadratic Urysohn integral equation on unbounded interval. The method used in our considerations depends on suitable conjunction of the technique of measures of noncompactness with the classical Schauder fixed point principle. Such an approach permits us to obtain our existence results under rather general assumptions.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">255</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">HARK-MAHN KIM</style></author><author><style face="normal" font="default" size="100%">SHEON-YOUNG KANG</style></author><author><style face="normal" font="default" size="100%">ICK-SOON CHANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE STABILITY FOR CUBIC FUNCTIONAL EQUATION OF MIXED TYPE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39B52</style></keyword><keyword><style  face="normal" font="default" size="100%">39B72</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-583-594.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we consider the general solution for a mixed type cubic functional equation lf( mX−1 i=1 xi + lxm) + lf( mX−1 i=1 xi − lxm) + 2 mX−1 i=1 f(lxi) = 2lf( mX−1 i=1 xi) + l 3 mX−1 i=1 [f(xi + xm) + f(xi − xm)], where l ≥ 2 and m ≥ 3 are any integers and investigate the Hyers-Ulam-Rassias stability of this equation.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">583</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">LEONID SHAIKHET</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STABILITY OF A POSITIVE POINT OF EQUILIBRIUM OF ONE NONLINEAR SYSTEM WITH AFTEREFFECT AND STOCHASTIC PERTURBATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34D20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-235-254.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">19</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The aim of the paper is to show one useful way for stability investigation of the positive point of equilibrium of some nonlinear system with aftereffect and stochastic perturbations. Obtained results are applied for stability investigation of some mathematical predator-prey models.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">235</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">YOU-WEI ZHANG</style></author><author><style face="normal" font="default" size="100%">HONG-RUI SUN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THREE POSITIVE SOLUTIONS FOR A GENERALIZED STURM-LIOUVILLE MULTIPOINT BVP WITH DEPENDENCE ON THE FIRST ORDER DERIVATIVE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-313-324.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we are concerned with the following generalized Sturm-Liouville multipoint boundary value problem u 00(t) + h (t) f (t, u (t), u 0 (t)) = 0, 0 &amp;lt; t &amp;lt; 1, au (0) − bu0 (0) = mX−2 i=1 aiu(ξi), cu (1) + du0 (1) = mX−2 i=1 biu(ξi), where 0 &amp;lt; ξ1 &amp;lt; · · · &amp;lt; ξm−2 &amp;lt; 1 (m ≥ 3), a, b, c, d ∈ [0, ∞), ai , bi ∈ (0, ∞) (i = 1, 2, . . . , m − 2) are constants satisfying some suitable conditions. Existence criteria for at least three positive solutions are established by using the fixed point theorem of Avery and Peterson. The interesting point is the nonlinear term f which is involved with the first order derivative explicitly.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">313</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">YU TIAN</style></author><author><style face="normal" font="default" size="100%">WEIGAO GE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">TRIPLE POSITIVE SOLUTIONS OF THREE-POINT BOUNDARY VALUE PROBLEM FOR SECOND-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS ON THE HALF-LINE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A37</style></keyword><keyword><style  face="normal" font="default" size="100%">34B37</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-637-652.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we consider the existence of triple positive solutions for second-order three-point boundary value problem with impulse effects on the half-line. Main results are besed on fixed point theorem on cone. In particular, the nonlinear term is involved with the first-order derivative.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">637</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MICHAL KISIELEWICZ</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">WEAK COMPACTNESS OF WEAK SOLUTIONS TO BACKWARD STOCHASTIC DIFFERENTIAL INCLUSIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-351-370.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Weak compactness with respect to weak converegence in the Meyer-Zheng topology of sets of all weak solutions to backward stochastic differential inclusions is considered. Some existence theorems for backward stochastic differential inclusions are also given.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">351</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MICHA  KISIELEWICZ</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">BACKWARD STOCHASTIC DIFFERENTIAL INCLUSIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H04</style></keyword><keyword><style  face="normal" font="default" size="100%">49J53</style></keyword><keyword><style  face="normal" font="default" size="100%">60H05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/121-140-New-Kisielewicz-1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">19</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Existence of solutions to backward stochastic differential inclusions is considered. The paper contains the basic notions dealing with backward stochastic differential inclusions.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">121</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BO ZHANG</style></author><author><style face="normal" font="default" size="100%">JING XU</style></author><author><style face="normal" font="default" size="100%">D. KANNAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A BACKWARDS STOCHASTIC DIFFERENTIAL EQUATION MODEL IN LIFE INSURANCE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34F05</style></keyword><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/327-336-DSA-26-16-ZhangXuKannan.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this article we obtain the ratio of risk investment and the optimal accumulated level of single premium endowment insurance in the case of dynamic investment strategies of life insurance company by BSDEs. It gives an illustration of traditional reserve valuation, and prudential rules.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">327</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">F. S. DE_BLASI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">BANACH-SAKS-MAZUR AND KAKUTANI-KY FAN THEOREMS IN SPACES OF MULTIFUNCTIONS AND APPLICATIONS TO SET DIFFERENTIAL INCLUSIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/073-088-New-De_blasi.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Some multivalued versions of the theorems of Banach-Saks-Mazur and Kakutani-Ky Fan are proved. These results are used in existence problems for set differential inclusions.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">73</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. AMRAOUI</style></author><author><style face="normal" font="default" size="100%">M. IGUERNANE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">BIFURCATION AT MULTIPLE EIGENVALUES FOR SYSTEMS WITH LIPSCHITZ MAPPINGS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">46B99</style></keyword><keyword><style  face="normal" font="default" size="100%">47A10</style></keyword><keyword><style  face="normal" font="default" size="100%">47A12</style></keyword><keyword><style  face="normal" font="default" size="100%">47A30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/187-202-DSA-25-09-Amraoui.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Some results on the existence of bifurcation at multiple eigenvalues for abstract systems concerning Lipschitz continuous mappings in Banach spaces are proved. The obtained results improve some well-known bifurcation results by Crandall and Rabinowitz, McLeod and Sattinger, Tan etc, in the case involving Lipschitz continuous mappings. An application to a system of partial differential equations will be given.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">187</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JAN ANDRES</style></author><author><style face="normal" font="default" size="100%">LUISA MALAGUTI</style></author><author><style face="normal" font="default" size="100%">VALENTINA TADDEI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A BOUNDING FUNCTIONS APPROACH TO MULTIVALUED BOUNDARY VALUE PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A60</style></keyword><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/037-048-Andres.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The solvability of Floquet boundary value problems is investigated for upper-Carathéodory differential inclusions by means of strictly localized C&lt;sup&gt;2&lt;/sup&gt; -bounding functions. The existence of an entirely bounded solution is obtained in a sequential way. Our criteria can be regarded as a multivalued extension of recent results of Mawhin and Thompson concerning periodic and bounded solutions of Carath´eodory differential equations. A simple illustrating example is supplied. Keywords and phrases: Floquet boundary value problems, upper-Carathéodory differential inclusions, bounding functions, bounded solutions.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">37</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">NAZIM  MAHMUDOV</style></author><author><style face="normal" font="default" size="100%">MARK  MCKIBBEN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON A CLASS OF BACKWARD MCKEAN-VLASOV STOCHASTIC EQUATIONS IN HILBERT SPACE: EXISTENCE AND CONVERGENCE PROPERTIES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/643-664-DSA-022.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">22</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This investigation is devoted to the study of a class of abstract first-order backward McKean-Vlasov stochastic evolution equations in a Hilbert space. Results concerning the existence and uniqueness of solutions and the convergence of an approximating sequence of solutions (and corresponding probability measures) are established. Examples that illustrate the abstract theory are also provided.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">643</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ALEXANDER  ZASLAVSKI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON A CLASS OF SECOND ORDER INFINITE HORIZON VARIATIONAL PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">49J99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/517-532-Zaslavski.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we consider a class of one-dimensional variational problems arising in continuum mechanics which are defined on infinite intervals. We are interested in the existence of non-constant periodic minimizers for these problems.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">517</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">G.C. LI</style></author><author><style face="normal" font="default" size="100%">S.J. SONG</style></author><author><style face="normal" font="default" size="100%">B. ZHANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">CONTROLLABILITY OF NONLINEAR INTEGRODIFFERENTIAL SYSTEMS IN BANACH SPACE WITH NONLOCAL CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/729-742-DSA-046.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Sufficient conditions for controllability of nonlinear integrodifferential systems in a separable Banach space with nonlocal conditions are established. The results are obtained using a compactness type hypothesis involving the Hausdorff-measure of noncompactness, Kakutani’s fixedpoint theorem and Schauder’s fixed-point theorem.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">729</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">TADEUSZ JANKOWSKI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON DELAY DIFFERENTIAL EQUATIONS WITH BOUNDARY CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A45</style></keyword><keyword><style  face="normal" font="default" size="100%">34K10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/425-432-Jankowski.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Some existence results are formulated for delay differential problems with boundary conditions assuming monotonicity of functions on the right hand side of our problem. It is shown that two monotone sequences converge to corresponding limit functions.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">425</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">N. U. AHMED</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">DIFFERENTIAL INCLUSIONS OPERATOR VALUED MEASURES AND OPTIMAL CONTROL</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34G20</style></keyword><keyword><style  face="normal" font="default" size="100%">34K30</style></keyword><keyword><style  face="normal" font="default" size="100%">35A05</style></keyword><keyword><style  face="normal" font="default" size="100%">93C25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/013-036-Ahmed.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">23</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The objective of this paper is to briefly summarize some recent results on Differential Inclusions and their optimal control. Then, using vector measures as controls, we present some new results on the necessary conditions of optimality. Further, we consider systems having structural perturbation modeled by operator valued measures. The paper is concluded indicating some open problems.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">13</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SVETLANA  AZARINA</style></author><author><style face="normal" font="default" size="100%">YURI GLIKLIKH</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">DIFFERENTIAL INCLUSIONS WITH MEAN DERIVATIVES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A60</style></keyword><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword><keyword><style  face="normal" font="default" size="100%">60H99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/049-072-Azarina.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">23</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We introduce and investigate a new sort of stochastic differential inclusions given in terms of mean derivatives of a stochastic process, introduced by E. Nelson for the needs of the so called stochastic mechanics. This class of stochastic inclusions is ideologically the closest one to ordinary differential inclusions. We consider three types of inclusions: with forward mean derivatives, with backward mean derivatives and with current velocities (symmetric mean derivatives). These types have different properties and physical meaning. Some existence of solutions results are proved.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">49</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RAVI  AGARWAL</style></author><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author><author><style face="normal" font="default" size="100%">RADU PRECUP</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">DOMAIN INVARIANCE THEOREMS FOR CONTRACTIVE TYPE MAPS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/579-586-Agarwal.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;New domain invariance theorems are presented for nonlinear contractions on spaces with two metrics.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">579</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RAVI  AGARWAL</style></author><author><style face="normal" font="default" size="100%">HAROLD  THOMPSON</style></author><author><style face="normal" font="default" size="100%">CHRISTOPHER TISDELL</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE EXISTENCE OF MULTIPLE SOLUTIONS TO BOUNDARY VALUE PROBLEMS FOR SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/595-609-Agarwal.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We establish existence results for multiple solutions to boundary value problems for nonlinear, second order, ordinary differential equations subject to nonlinear boundary conditions involving two points. We apply our theory to a problem from chemical reactor theory. Our results are extended to systems of equations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">595</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JIAN-PING SUN</style></author><author><style face="normal" font="default" size="100%">WAN-TONG LI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF POSITIVE SOLUTIONS TO SEMIPOSITONE DIRICHLET BVPS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/571-578-SunLi.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we are concerned with the following semipositone Dirichlet boundary value problem on a time scale T ( −u ∆∆(t) = g(t, u(t)), t ∈ [0, T]T, u(0) = 0 = u(σ 2 (T)), where g : [0, T]T × [0, +∞) → [−M, +∞) is continuous and M &amp;gt; 0 is a constant. Some existence criteria for at least one positive solution are established by using well-known results from fixed point index theory.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">571</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">GARY JONES</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF SOLUTIONS OF MULTIPOINT BOUNDARY VALUE PROBLEMS FOR A SECOND ORDER DIFFERENTIAL EQUATION</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/709-712-DSA-043.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">3</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Assuming the uniqueness of an n-point boundary value problem, for some n ≥ 4 for&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;y'' = f(x, y, y' )&lt;/p&gt;

&lt;p&gt;existence of unique solutions are proved for all n ≥ 2.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">709</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">C.Y. CHAN</style></author><author><style face="normal" font="default" size="100%">H.T. LIU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE, UNIQUENESS AND QUENCHING OF THE SOLUTION FOR A NONLOCAL DEGENERATE SEMILINEAR PARABOLIC PROBLEM</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35K57</style></keyword><keyword><style  face="normal" font="default" size="100%">35K60</style></keyword><keyword><style  face="normal" font="default" size="100%">35K65</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/551-560-Chan.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let a and T be positive constants, D = (0, a), D¯ = [0, a], Ω = D × (0, T], and Lu = x qut − uxx, where q is a nonnegative number. This article studies the following problem, Lu(x,t) = Zx 0 k(y)f(u(y,t))dy in Ω, where k is a positive function on D¯, f &amp;gt; 0, f 0≥ 0, f 00≥ 0, and limu→1− f(u) = ∞, subject to the initial condition u(x, 0) = 0 on D¯, and the boundary conditions u(0,t) = 0 = u(a,t) for 0 &amp;lt; t ≤ T. Existence of a unique solution, the critical length, and the quenching behavior of the solution are studied.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">551</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">B.C. DHAGE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">FIRST ORDER IMPULSIVE DIFFERENTIAL INCLUSIONS INVOLVING DISCONTINUOUS MULTIFUNCTIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A60</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/285-298-DSA-26-13-Dhage.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The present paper studies the existence as well as existence of the extremal solutions for the first order impulsive differential inclusions under generalized monotonic conditions and without assuming any kind of continuity of the multi-functions on the right hand side.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">285</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. HEIKKILÄ</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">FIXED POINT RESULTS FOR MULTIFUNCTIONS IN ORDERED TOPOLOGICAL SPACES WITH APPLICATIONS TO INCLUSION PROBLEMS AND TO GAME THEORY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H04</style></keyword><keyword><style  face="normal" font="default" size="100%">47H07</style></keyword><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword><keyword><style  face="normal" font="default" size="100%">91A06</style></keyword><keyword><style  face="normal" font="default" size="100%">91A44</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/105-120-Heikkila.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We prove existence results for minimal and maximal fixed points of multifunctions in ordered topological spaces, and apply the obtained results to study the solvability of inclusion problems and the existence of extremal Nash equilibria for normal-form games.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">105</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DUNG LE</style></author><author><style face="normal" font="default" size="100%">TOAN NGUYEN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">GLOBAL ATTRACTORS AND UNIFORM PERSISTENCE FOR CROSS DIFFUSION PARABOLIC SYSTEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35B65</style></keyword><keyword><style  face="normal" font="default" size="100%">35K65</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/361-378-DSA-26-20-LeNguyen.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A class of cross diffusion parabolic systems given on bounded domains of R&lt;sup&gt;n&lt;/sup&gt; , with arbitrary n, is investigated. We show that there is a global attractor with finite Hausdorff dimension which attracts all solutions. The result will be applied to the generalized Shigesada, Kawasaki and Teramoto (SKT) model with Lotka-Volterra reactions. In addition, the persistence property of the SKT model will be studied.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">361</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JUNG-CHAN CHANG</style></author><author><style face="normal" font="default" size="100%">CHENG-LIEN LANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">GLOBAL EXISTENCE FOR RETARDED VOLTERRA INTEGRODIFFERENTIAL EQUATIONS WITH HILLE-YOSIDA OPERATORS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/625-642-DSA-019.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we study the existence and uniqueness of classical global solutions of some integrodifferential equations with infinite delay. We loosen the conditions of the integral term in the equations which are more general than those that have been mentioned in many previous studies. Some sufficient conditions are given which ensure the existence and uniqueness of solutions on [0, ∞). We assume linear part is not necessary to be densely defined and satisfies a Hille-Yosida condition. By using matrix operators and fixed point theorems, we obtain new results for the retarded integrodifferential equations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">625</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">M.A. BOKHARI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON HERMITE INTERPOLATING L2-APPROXIMANTS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">05E35</style></keyword><keyword><style  face="normal" font="default" size="100%">41A29</style></keyword><keyword><style  face="normal" font="default" size="100%">42C05</style></keyword><keyword><style  face="normal" font="default" size="100%">65D05</style></keyword><keyword><style  face="normal" font="default" size="100%">65F25</style></keyword><keyword><style  face="normal" font="default" size="100%">93E24</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/203-216-DSA-25-67_Bokhari.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider L&lt;sub&gt;2&amp;nbsp;&lt;/sub&gt;-appoximation of a real-valued square integrable function by polynomials that satisfy certain Hermite interpolation conditions. The solution of the modified minimization problem is found by constructing an orthogonal basis of the underlying approximating subspace. A convergence problem related to the best approximants is considered in a restricted set-up. Some computational aspects based on discretization of the underlying measure are also discussed in detail&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">203</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BASHIR AHMAD</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">INTEGRO-DIFFERENTIAL EQUATIONS WITH INITIAL TIME DIFFERENCE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34D10</style></keyword><keyword><style  face="normal" font="default" size="100%">34D99</style></keyword><keyword><style  face="normal" font="default" size="100%">45J05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/497-506-Ahmad.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We apply Lakshmikantham’s generalized quasilinearization method to an initial value problem involving a nonlinear integro-differential equation with initial time difference and obtain monotone sequences of lower and upper solutions converging uniformly and quadratically to the unique solution of the problem.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">497</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">YURI  ROGOVCHENKO</style></author><author><style face="normal" font="default" size="100%">FATOS TUNCAY</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">INTERVAL OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH DAMPING</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/337-344-DSA-26-17-Rogovchenko.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">7</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Using generalized Riccati transformations, for a second order nonlinear differential equation with a damping term we derive nontrivial extensions of oscillation criteria obtained for linear equations by Kong [J. Math. Anal. Appl. 229 (1999), 258–270]. Efficiency of new results is illustrated on the example extracted from the recent paper by Sun [J. Math. Anal. Appl. 291 (2004), 341–351].&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">337</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">AIJUN DU</style></author><author><style face="normal" font="default" size="100%">JINQIAO DUAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">INVARIANT MANIFOLD REDUCTION FOR STOCHASTIC DYNAMICAL SYSTEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C45</style></keyword><keyword><style  face="normal" font="default" size="100%">34F05</style></keyword><keyword><style  face="normal" font="default" size="100%">37H10</style></keyword><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/681-696-DSA-039.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Invariant manifolds facilitate the understanding of nonlinear stochastic dynamics. When an invariant manifold is represented approximately by a graph for example, the whole stochastic dynamical system may be reduced or restricted to this manifold. This reduced system may provide valuable dynamical information for the original system. The authors have derived an invariant manifold reduction or restriction principle for systems of Stratonovich or Ito stochastic differential equations. Two concepts of invariance are considered for invariant manifolds. The first invariance concept is in the framework of cocycles - an invariant manifold being a random set. The dynamical reduction is achieved by investigating random center manifolds. The second invariance concept is in the sense of almost sure - an invariant manifold being a deterministic set which is not necessarily attracting. The restriction of the original stochastic system on this deterministic local invariant manifold is still a stochastic system but with reduced dimension&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">681</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RAVI AGARWAL</style></author><author><style face="normal" font="default" size="100%">YEOL-JE CHO</style></author><author><style face="normal" font="default" size="100%">HENG-YOU LAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ITERATIVE APPROXIMATIONS OF SOLUTIONS FOR SYSTEMS OF NONLINEAR OPERATOR EQUATIONS IN BANACH SPACES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword><keyword><style  face="normal" font="default" size="100%">47H15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/379-392-DSA-01-AgarwalChoLan.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, by virtue of the Mann iterative technique, we introduce and study a class of systems of nonlinear equations without any mixed monotone property and continuity, and prove the existence, uniqueness and Mann iterative approximation theorems of solutions for systems of nonlinear operator equations. The results presented in this paper improve and generalize the corresponding results of the earlier and recent works.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">379</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RAVI P. AGARWAL</style></author><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A LEFSCHETZ FIXED POINT THEOREM FOR ADMISSIBLE MAPS IN FRECHET ´ SPACES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/001-012-Agarwal.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The Lefschetz fixed point theorem is discussed for the admissible maps of Gorniewicz defined on admissible subsets of a Hausdorff topological space. Also using the projective limit approach we present new Lefschetz fixed point theorems for the admissible maps of Gorniewicz defined on PRLF’s or CPRLF’s.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">1</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">R. HILSCHER</style></author><author><style face="normal" font="default" size="100%">V. ZEIDAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">LEGENDRE, JACOBI, AND RICCATI TYPE CONDITIONS FOR TIME SCALE VARIATIONAL PROBLEM WITH APPLICATION</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A12</style></keyword><keyword><style  face="normal" font="default" size="100%">49K99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/451-480-Hilscher.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">30</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A time scale quadratic problem J with piecewise right-dense continuous coefficients and one varying endpoint is considered. Such problems are “hybrid”, since they include mixing of continuous- and discrete-time problems. A new notion of a generalized conjugate point involving “dynamic” (hybrid) systems and comprising as special cases those known for the continuous- and discrete-time settings is introduced. A type of a strengthened Legendre condition is identified and used to establish characterizations of the nonnegativity and positivity of J in terms of (i) the nonexistence of such conjugate points, (ii) the natural conjoined basis of the associated time scale Jacobi equation, and (iii) a solution of the corresponding time scale Riccati equation. These results furnish second order necessary optimality conditions for a nonlinear time scale variational problem. Furthermore, we present an example of an optimal impulsive control problem and we show how this problem can be reduced to a variational problem over a time scale.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">451</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JOHN GUARDIOLA</style></author><author><style face="normal" font="default" size="100%">GIUSEPPE IZZO</style></author><author><style face="normal" font="default" size="100%">ANTONIA VECCHIO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A MATHEMATICAL MODEL SIMULATING THE EFFECT OF VACCINE INDUCED RESPONSES ON HIV-1 INFECTION</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/407-424-Guardiola.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We analyze the mathematical model of the dynamics of HIV-1 infection in an organism reported in [9]. The model consists of a set of second type delay Volterra Integral Equations and takes into account the induction upon vaccination of a humoral and/or cellular immune response; the existence of a distributed delay for intracellular life cycle of the virus and a maximal time period for which an infected cell is allowed to become productive. We perform the analysis of the qualitative behavior of the solution by proving its positivity, boundedness and by providing a threshold parameter whose value permits to predict whether the infection will spread in the organism or not. Some numerical examples are added even if most of numerical analysis of the model is carried out in [9].&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">407</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DAQING JIANG</style></author><author><style face="normal" font="default" size="100%">JIFENG CHU</style></author><author><style face="normal" font="default" size="100%">YING HE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MULTIPLE POSITIVE SOLUTIONS OF STURM-LIOUVILLE PROBLEMS FOR SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A37</style></keyword><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">34C25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/611-624-DSA-016.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper is devoted to study the existence of multiple positive solutions for the second order Sturm-Liouville problems with impulse effects. The proof is based on the theory of fixed point index in cones.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">611</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">F. CAMMAROTO</style></author><author><style face="normal" font="default" size="100%">A. CHINNÍ</style></author><author><style face="normal" font="default" size="100%">B.DI BELLA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MULTIPLE SOLUTIONS FOR A DIRICHLET PROBLEM INVOLVING THE P-LAPLACIAN</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/673-680-DSA-032.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">7</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we establish some multiplicity results for a Dirichlet problem related to a parametric equation involving the p-Laplacian operator. To this aim we make use of a recent local minima result of B. Ricceri.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">673</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">EVGENIA PAPAGEORGIOU</style></author><author><style face="normal" font="default" size="100%">NIKOLAOS PAPAGEORGIOU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON MULTIPLE SOLUTIONS FOR STRONGLY RESONANT PROBLEMS WITH THE p-LAPLACIAN</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35J20</style></keyword><keyword><style  face="normal" font="default" size="100%">35J60</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/175-186-Papageorgiou.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study a nonlinear elliptic problem driven by the p-Laplacian and with a nonsmooth potential function (hemivariational inequality). On the nonsmooth potential we impose conditions of strong resonance. Following a variational approach based on the nonsmooth critical point theory and the second deformation theorem, we establish the existence of at least two nontrivial smooth solutions.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">175</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">EUN-KYOUNG LEE</style></author><author><style face="normal" font="default" size="100%">YONG-HOON LEE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MULTIPLICITY RESULTS OF POSITIVE SOLUTIONS FOR SINGULAR BOUNDARY VALUE PROBLEMS WITH TIME DEPENDENT NONLINEARITY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A37</style></keyword><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/233-250-DSA-26-06-Lee.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We investigate bifurcation phenomena of positive solutions for problems of the form; u 00(t) + λf(t, u(t)) = 0, t ∈ (0, 1), u(0) = 0 = u(1), when f satisfies that there exists r ∈ C((0, 1),(0, ∞)) with R1 0 s(1 − s)r(s)ds &amp;lt; ∞ such that 0 &amp;lt; limu→0+ f(t,u) r(t)u &amp;lt; ∞ uniformly in t ∈ (0, 1). Here λ is a positive real parameter and f ∈ C((0, 1) × [0, ∞), [0, ∞)) may be singular at t = 0 and/or t = 1.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">233</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">B.G. ZHANG</style></author><author><style face="normal" font="default" size="100%">YONG ZHOU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NEW OSCILLATIONS CRITERIA OF DELAY PARTIAL DIFFERENCE EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/267-276-DSA-26-09-Zhang.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Consider the delay partial difference equation Am+1,n + Am,n+1 − Am,n + Xu i=1 Pi(m, n)Am−ki,n−li = 0, m, n ∈ N0, where lim infm,n→∞ Pi(m, n) = pi ∈ [0, ∞), ki , li ∈ N1, i = 1, 2, . . . , u. Sufficient conditions for the oscillation of all solutions of the above equation are established in the case when that the corresponding “limiting” equation Am+1,n + Am,n+1 − Am,n + Xu i=1 piAm−ki,n−li = 0, m, n ∈ N0, admits non-oscillatory solutions. Oscillation criteria for nonlinear partial difference equation are also derived as applications.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">267</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">STANISLAW MIGÓRSKI</style></author><author><style face="normal" font="default" size="100%">ANNA OCHAL</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NONLINEAR IMPULSIVE EVOLUTION INCLUSIONS OF SECOND ORDER</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A37</style></keyword><keyword><style  face="normal" font="default" size="100%">34G20</style></keyword><keyword><style  face="normal" font="default" size="100%">35A05</style></keyword><keyword><style  face="normal" font="default" size="100%">35L70</style></keyword><keyword><style  face="normal" font="default" size="100%">47H04</style></keyword><keyword><style  face="normal" font="default" size="100%">93C25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/155-174-Migorski.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">19</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we consider strongly nonlinear second order impulsive evolution inclusions. We provide the existence results for the Cauchy problems with convex and nonconvex valued right hand sides. The compactness of the solution set in the convex case is proved. Applications to a distributed parameter control system with a priori feedback and to a hyperbolic hemivariational inequality with impulses are provided.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">155</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Y. PENG</style></author><author><style face="normal" font="default" size="100%">X. XIANG</style></author><author><style face="normal" font="default" size="100%">W. WEI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NONLINEAR IMPULSIVE INTEGRO-DIFFERENTIAL EQUATIONS OF MIXED TYPE WITH TIME-VARYING GENERATING OPERATORS AND OPTIMAL CONTROLS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34G20</style></keyword><keyword><style  face="normal" font="default" size="100%">34K30</style></keyword><keyword><style  face="normal" font="default" size="100%">35B62</style></keyword><keyword><style  face="normal" font="default" size="100%">93C25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/481-496-Peng.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Nonlinear impulsive integro-differential equations of mixed type with time-varying generating operators is considered. Existence of PC − α-mild solutions is proved. Existence of optimal pairs of systems governed by impulsive integro-differential equations of mixed type is also presented. An example is given for demonstration.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">481</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">P. BALASUBRAMANIAM</style></author><author><style face="normal" font="default" size="100%">J.Y. PARK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NONLOCAL CAUCHY PROBLEM FOR SECOND ORDER STOCHASTIC EVOLUTION EQUATIONS IN HILBERT SPACES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34F05</style></keyword><keyword><style  face="normal" font="default" size="100%">49K24</style></keyword><keyword><style  face="normal" font="default" size="100%">60G12</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/713-728-DSA-045.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Existence of mild solutions of second order nonlinear stochastic evolution equations with nonlocal conditions in Hilbert spaces is established. The results are obtained by using the Schaefer fixed point theorem. Application for the beam equation is also discussed to illustrate the theory.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">713</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RAVI  AGARWAL</style></author><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author><author><style face="normal" font="default" size="100%">RADU PRECUP</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NONUNIFORM NONRESONANCE FOR NONLINEAR BOUNDARY VALUE PROBLEMS WITH y' DEPENDENCE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/587-594-Agarwal.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A new nonuniform nonresonant result at the first eigenvalue is presented for the boundary value problem y''+ q f(t, y, y' ) = 0&amp;nbsp; a.e. on [0, 1], y(0) = y(1) = 0.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">587</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BARUCH CAHLON</style></author><author><style face="normal" font="default" size="100%">DARRELL SCHMIDT</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NOTE ON ASYMPTOTIC STABILITY OF A MECHANICAL ROBOTICS MODEL WITH DELAY AND NEGATIVE AND POSITIVE DAMPING</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34D99</style></keyword><keyword><style  face="normal" font="default" size="100%">45E99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/311-326-DSA-26-15_Cahlon.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we study the asymptotic stability of a mechanical robotics model with damping and delay. In this paper we deal with a more realistic damping model than that considered in a previous paper [5]. This model yields a certain linear third order delay differential equation. In proving our results we make use of Pontryagin’s theory for quasi-polynomials.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">311</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Z.G. FENG</style></author><author><style face="normal" font="default" size="100%">K.L. TEO</style></author><author><style face="normal" font="default" size="100%">N.U. AHMED</style></author><author><style face="normal" font="default" size="100%">Y. ZHAO</style></author><author><style face="normal" font="default" size="100%">W.Y. YAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OPTIMAL FUSION OF SENSOR DATA FOR DISCRETE KALMAN FILTERING</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/393-406-DSA-25-53-58%20NU%20Ahmed.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we consider the question of optimal fusion of sensor data in discrete time. The basic problem is to design a linear filter whose output provides an unbiased minimum variance estimate of a signal process whose noisy measurements from multiple sensors are available for input to the filter. The problem is to assign weights to each of the sources (sensor data) dynamically so as to minimize estimation errors. We formulate the problem as an optimal control problem where the weight given to each of the sensor data is considered as one of the control variables satisfying certain constraints. There are as many controls as there are sensors. We develop an efficient method for determining the optimal fusion strategy and gives a numerical result for illustration.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">393</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">C. GORI</style></author><author><style face="normal" font="default" size="100%">V. OBUKHOVSKI</style></author><author><style face="normal" font="default" size="100%">P. RUBBIONI</style></author><author><style face="normal" font="default" size="100%">V. ZVYAGIN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OPTIMIZATION OF THE MOTION OF A VISCO-ELASTIC FLUID VIA MULTIVALUED TOPOLOGICAL DEGREE METHOD</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H04</style></keyword><keyword><style  face="normal" font="default" size="100%">47H09</style></keyword><keyword><style  face="normal" font="default" size="100%">47H11</style></keyword><keyword><style  face="normal" font="default" size="100%">76A05</style></keyword><keyword><style  face="normal" font="default" size="100%">76A10</style></keyword><keyword><style  face="normal" font="default" size="100%">76D55</style></keyword><keyword><style  face="normal" font="default" size="100%">93B52</style></keyword><keyword><style  face="normal" font="default" size="100%">93C20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/089-104-Gori.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider the application of the topological degree theory for noncompact multivalued vector fields to the problem of existence of an optimal feedback control in the presence of delay for the model of the motion of a visco-elastic fluid satisfying the Voight rheological relation. The notion of a weak solution to the problem is introduced and the operator treatment of the problem allows to reduce it to the existence of a fixed point for a certain condensing multivalued map. We give an a priori estimate for solutions of the problem and the use of the degree method allows to prove the non-voidness and compactness of the solution set. As the result we obtain the existence of a solution minimizing the given quality functional.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">89</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">FANWEI MENG</style></author><author><style face="normal" font="default" size="100%">CUIQIN MA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OSCILLATION OF LINEAR SECOND ORDER MATRIX DIFFERENTIAL SYSTEMS WITH DAMPING</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">34K15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/433-450-Meng.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, sufficient conditions have been obtained for the oscillation of a class of linear second order matrix differential systems with damping.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">433</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S.H. SAKER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OSCILLATION OF SECOND-ORDER DELAY AND NEUTRAL DELAY DYNAMIC EQUATIONS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A99</style></keyword><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">34K11</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A11</style></keyword><keyword><style  face="normal" font="default" size="100%">39A99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/345-360-DSA-26-18-Saker.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we consider the second-order linear delay dynamic equation x ∆∆(t) + q(t)x(τ (t)) = 0, on a time scale T. We will study the properties of the solutions and establish some sufficient conditions for oscillations. In the special case when T = R and τ (t) = t, our results include some well-known results in the literature for differential equations. When, T = Z, T = hZ, for h &amp;gt; 0 and T = Tn = {tn : n ∈ N0} where tn} is the set of the harmonic numbers defined by t0 = 0, tn = Pn k=1 1 k for n ∈ N0 our results are essentially new. The results will be applied on second-order neutral delay dynamic equations in time scales to obtain some sufficient conditions for oscillations. An example is considered to illustrate the main results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">345</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RAVI AGARWAL</style></author><author><style face="normal" font="default" size="100%">SVATOSLAV STANEK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">POSITIVE SOLUTIONS OF SINGULAR BOUNDARY VALUE PROBLEMS FOR DELAY DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Existence criteria are established for positive solutions of singular boundary value problems for nonlinear second order ordinary and delay differential equations. Here the nonlinearities may be singular at phase variables and positive solutions ‘pass through’ the singularities.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">755</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ONDREJ  DOSLY</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">RECIPROCITY PRINCIPLE FOR EVEN-ORDER DYNAMIC EQUATIONS WITH MIXED DERIVATIVES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A12</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/697-708-DSA-041.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We establish the equivalence of oscillatory behavior of a certain pair of even-order time scale dynamic equations with mixed derivatives. For the special time scales T = R and T = N, this statement is usually referred to as the reciprocity principle.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">697</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MARK ELIN</style></author><author><style face="normal" font="default" size="100%">MARINA LEVENSHTEIN</style></author><author><style face="normal" font="default" size="100%">DAVID SHOIKHET</style></author><author><style face="normal" font="default" size="100%">ROBERTO TAURASO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">RIGIDITY OF HOLOMORPHIC GENERATORS AND ONE-PARAMETER SEMIGROUPS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">30D05</style></keyword><keyword><style  face="normal" font="default" size="100%">32H12</style></keyword><keyword><style  face="normal" font="default" size="100%">47B33</style></keyword><keyword><style  face="normal" font="default" size="100%">47H20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/251-266-DSA-26-08-Elin.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we establish a rigidity property of holomorphic generators by using their local behavior at a boundary point τ of the open unit disk ∆. Namely,&amp;nbsp; if f ∈ Hol(∆, C) is the generator of a&amp;nbsp; one- parameter continuous semigroup&amp;nbsp; {F&lt;sub&gt;t&lt;/sub&gt; }&lt;sub&gt;t&amp;nbsp;&lt;/sub&gt;≥ 0, we show that the equality f(z) = o (|z − τ |&lt;sup&gt;3&lt;/sup&gt;)&amp;nbsp;when z → τ in each non-tangential approach region at τ implies that f vanishes identically on ∆. Note, that if F is a self-mapping of ∆ then f = I − F is a generator, so our result extends the boundary version of the Schwarz Lemma obtained by D. Burns and S. Krantz. We also prove that two semigroups &amp;nbsp;{ F&lt;sub&gt;t&lt;/sub&gt; }&lt;sub&gt;t&amp;nbsp;&lt;/sub&gt;≥ 0 and { G&lt;sub&gt;t&lt;/sub&gt; }&lt;sub&gt;t&amp;nbsp;&lt;/sub&gt;≥ 0, with generators f and g respectively, commute if and only if the equality f = αg holds for some complex constant α. This fact gives simple conditions on the generators of two commuting semigroups at their common null point τ under which the semigroups coincide identically on ∆.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">251</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">B.C. DHAGE</style></author><author><style face="normal" font="default" size="100%">S.K. NTOUYAS</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SECOND ORDER CARATHEODORY AND DISCONTINUOUS INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH ALGEBRAS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A12</style></keyword><keyword><style  face="normal" font="default" size="100%">34K05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/217-232-DSA-26-03-B.%20C.%20Dhage%20BCD-SKN.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper an existence theorem for the second order integro-differential equations in Banach algebras is proved under the mixed generalized Lipschitz and Carath´eodory conditions. The existence of extremal solutions is also proved under certain monotonicity conditions.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">217</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DELKADER BOUCHERIF</style></author><author><style face="normal" font="default" size="100%">RADU PRECUP</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SEMILINEAR EVOLUTION EQUATIONS WITH NONLOCAL INITIAL CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34G20</style></keyword><keyword><style  face="normal" font="default" size="100%">47D06</style></keyword><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword><keyword><style  face="normal" font="default" size="100%">47N20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/507-516-Boucherif.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We are concerned with the study of semilinear evolution equations with nonlocal initial conditions. We provide sufficient conditions on the nonlinearity which allow the use of variants of the nonlinear alternative to prove the existence of at least one solution. Our second result presents a novel growth condition splitted into two parts, one for the subinterval containing the points involved by the initial conditions, and another for the rest of the interval.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">507</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MARIUSZ MICHTA</style></author><author><style face="normal" font="default" size="100%">JERZY MOTYL</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SET VALUED STRATONOVICH INTEGRAL AND STRATONOVICH TYPE STOCHASTIC INCLUSION</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H04</style></keyword><keyword><style  face="normal" font="default" size="100%">49J53</style></keyword><keyword><style  face="normal" font="default" size="100%">60H05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/141-154-MichtaMotyl.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In the paper we discuss the construction of a set-valued stochastic integral of the Stratonovich type driven by a semimartingale. It allows to consider the stochastic inclusion of a type of Stratonovich. The existence of strong solutions to such inclusion with upper separated set-valued functions is investigated.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">141</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BASHIR AHMAD</style></author><author><style face="normal" font="default" size="100%">S. SIVASUNDARAM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SETVALUED PERTURBED HYBRID INTEGRO-DIFFERENTIAL EQUATIONS AND STABILITY IN TERMS OF TWO MEASURES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K20</style></keyword><keyword><style  face="normal" font="default" size="100%">34K25</style></keyword><keyword><style  face="normal" font="default" size="100%">45J05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/299-310-DSA-26-14-Ahmad.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study some stability criteria in terms of two measures for setvalued perturbed hybrid integro-differential equations with fixed moments of impulse. Stability properties of perturbed system are obtained via a comparison result which connects the solutions of perturbed system and the unperturbed one through the solutions of a comparison system.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">299</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ERIC KAUFMANN</style></author><author><style face="normal" font="default" size="100%">YOUSSEF  RAFFOUL</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STABILITY IN NEUTRAL NONLINEAR DYNAMIC EQUATIONS ON A TIME SCALE WITH FUNCTIONAL DELAY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K20</style></keyword><keyword><style  face="normal" font="default" size="100%">34K30</style></keyword><keyword><style  face="normal" font="default" size="100%">34K40</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/561-570-Kaufmann.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let T be a time scale that is unbounded above and below and such that 0 ∈ T. Let τ : T → T be such that τ (T) is a time scale. We use fixed point theorems to obtain stability results about the zero solution of the nonlinear neutral dynamic equation with functional delay&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; x&lt;sup&gt;∆&lt;/sup&gt;(t) = −a(t) x&lt;sup&gt;σ&lt;/sup&gt;(t) + c(t) x&lt;sup&gt;∆˜&lt;/sup&gt;( τ (t) ) + q( x(t), x( τ (t)) ) ,&amp;nbsp; &amp;nbsp;t ∈ T,&lt;/p&gt;

&lt;p&gt;where f&lt;sup&gt;∆&lt;/sup&gt; is the ∆-derivative on T and f&lt;sup&gt;∆˜&lt;/sup&gt; is the ∆-derivative on τ (T).&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">561</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">YANSHENG LIU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">TRIPLE POSITIVE SOLUTIONS OF NONLINEAR SINGULAR STURM-LIOUVILLE BOUNDARY VALUE PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B16</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/533-550-Liu.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper presents a new theorem on the existence of triple nontrivial fixed points and then investigates the existence of triple positive solutions of a class of nonlinear singular boundary value problem by using this new fixed point theorem. Meanwhile, an example is worked out to demonstrate the main result.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">533</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MICHAEL GRAY</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">UNIQUENESS IMPLIES UNIQUENESS FOR NONLOCAL BOUNDARY VALUE PROBLEMS FOR THIRD ORDER ORDINARY DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/277-284-DSA-26-12-Gray.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;It is assumed that solutions of the differential equation y''' = f( x, y, y', y'' ), with certain boundary conditions comprised of function values at m + n points, are unique, when they exist. It is shown that, for any integers p and q such that 1 ≤ p ≤ m,&amp;nbsp; 1 &amp;lt; q ≤ n,&amp;nbsp; solutions for similar boundary value problems are unique, when they exist.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">277</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DAQING JIANG</style></author><author><style face="normal" font="default" size="100%">P. Y. H. PANG</style></author><author><style face="normal" font="default" size="100%">RAVI AGARWAL</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">UPPER AND LOWER SOLUTIONS METHOD AND A SUPERLINEAR SINGULAR DISCRETE BOUNDARY VALUE PROBLEM</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B16</style></keyword><keyword><style  face="normal" font="default" size="100%">39A99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/743-754-Ravi-05.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we study the singular discrete boundary value problem    ∆[φ(∆u(t − 1))] + g(t, u(t)) = 0, t ∈ {1, 2, . . . , T}, u(0) = u(T + 1) = 0 where φ(s) = |s| p−2 s, p &amp;gt; 1, and the function g is superlinear at infinity and may change sign or be singular at u = 0. Existence of solutions is obtained via an upper and lower solutions method.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">743</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MOHAMED MEDJDEN</style></author><author><style face="normal" font="default" size="100%">NASSER-EDDINE TATAR</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE WAVE EQUATION WITH A TEMPORAL NON-LOCAL TERM</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35B40</style></keyword><keyword><style  face="normal" font="default" size="100%">35L20</style></keyword><keyword><style  face="normal" font="default" size="100%">45K05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/665-672-DSA-026.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">7</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper is concerned with the asymptotic behavior for an integro-differential equation which appears in viscoelasticity. It is proved that the energy of the system decays exponentially to zero as time goes to infinity provided that the kernel in the memory term is also exponentially decaying. New assumptions are discussed.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">665</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SVETOSLAV MARKOV</style></author><author><style face="normal" font="default" size="100%">NIKOLAY KYURKCHIEV</style></author><author><style face="normal" font="default" size="100%">ANTON ILIEV</style></author><author><style face="normal" font="default" size="100%">ASEN RAHNEV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE APPROXIMATION OF THE GENERALIZED CUT FUNCTION OF DEGREE p+1 BY SMOOTH HYPER–LOG–LOGISTIC FUNCTION</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">41A46</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">208</style></year><pub-dates><date><style  face="normal" font="default" size="100%">09/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/4/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;We introduce a modification of the familiar cut function by replacing&amp;nbsp;the linear part in its definition by a polynomial of degree p + 1 obtaining thus a&amp;nbsp;sigmoid function called generalized cut function of degree p+1 (GCFP).We then study&amp;nbsp;the uniform approximation of the (GCFP) by smooth sigmoid functions such as the&amp;nbsp;hyper–log–logistic and the shifted hyper–log–logistic functions. The limiting case of&amp;nbsp;the interval-valued Heaviside step function is also discussed which imposes the use of&amp;nbsp;Hausdorff metric. Numerical examples are presented using CAS MATHEMATICA.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">715</style></section></record></records></xml>