<?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%">MUHAMMAD N. ISLAM</style></author><author><style face="normal" font="default" size="100%">JEFFREY T. NEUGEBAUER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ASYMPTOTIC STABILITY OF FUNCTIONAL EQUATIONS BY FIXED POINT THEOREMS</style></title></titles><keywords><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%">11/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/en/articles/22/4/8.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">22</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;For many years, Liapunov’s direct method has been the primary technique for studying various stability also known as ‘Liapunov stability’ of functional differential equations. Recently, it has been noticed that&amp;nbsp;some difficulties can arise when Liapunov’s method is applied to certain equations, and that a suitable fixed point theorem can overcome some of these&amp;nbsp;difficulties. In this paper we study a particular stability which differs from the&amp;nbsp;Liapunov stability. In particular, we study the existence of asymptotically stable solutions of a system of nonlinear Volterra integral equations. We employ&amp;nbsp;a fixed point theorem due to Krasnosel’skii in the analysis.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><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%">JEFFREY T. NEUGEBAUER</style></author><author><style face="normal" font="default" size="100%">CHARLEY L. SEELBACH</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A DIFFERENCE EQUATION WITH DIRICHLET BOUNDARY CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Applied Analysis</style></secondary-title><alt-title><style face="normal" font="default" size="100%">ЦАА</style></alt-title><short-title><style face="normal" font="default" size="100%">A Difference Equation with Dirichlet Boundary Conditions  </style></short-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%">03/2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/21/2/5.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">21</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;A recent Avery et al. fixed point theorem is applied to show the existence of a positive solution of the second order difference equation&lt;/p&gt;

&lt;p class=&quot;rtecenter&quot;&gt;$$\Delta^{2}u\left(k\right)+f\left(u\left(k\right)\right),\quad k\in\left\{0,1,...,N\right\},$$&lt;/p&gt;

&lt;p&gt;with boundary conditions&lt;/p&gt;

&lt;p class=&quot;rtecenter&quot;&gt;$$u\left(0\right)=u\left(N+2\right)=0.$$&lt;/p&gt;

&lt;p&gt;An example is also given.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><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%">PAUL ELOE</style></author><author><style face="normal" font="default" size="100%">JEFFREY W. LYONS</style></author><author><style face="normal" font="default" size="100%">JEFFREY T. NEUGEBAUER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">AN ORDERING ON GREEN’S FUNCTIONS FOR A FAMILY OF TWO-POINT BOUNDARY VALUE PROBLEMS FOR FRACTIONAL DIFFERENTIAL EQUATIONS</style></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%">34A40</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%">http://www.acadsol.eu/en/articles/19/3/10.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%">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 ${ 2 ≤ n }$&amp;nbsp; denote an integer and let ${ n−1 &amp;lt; α ≤ n.}$ For each ${0 &amp;lt; b, 0 ≤ β ≤ n−1 }$, the authors will construct the Green’s function,${ G(b, β;t, s),}$ of the two-point boundary value problem for the fractional differential equation $${ D^α_{0+}u + h(t) = 0, \ \ \ 0 &amp;lt; t &amp;lt; b, }$$ $${ u^{(i)} (0) = 0, \ \ \&amp;nbsp; i = 0, . . . n − 2, \ \ \ D^β_{0+}u(b) = 0,}$$ where ${ D^α_{0+} }$ and ${ D^β_{0+} }$ denote the standard Riemann-Liouville derivatives. The authors will compare Green’s functions, ${ G(b1, β;t, s) }$ and ${ G(b2, β;t, s) }$ or ${ G(b, β1;t, s)}$&amp;nbsp; and ${ G(b, β2;t, s),}$ and the authors will show the existence of a unique limiting function as ${ b → ∞.}$ An application to a nonlinear problem will be given.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">453</style></section></record></records></xml>