<?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%">SMITA PATI</style></author><author><style face="normal" font="default" size="100%">SESHADEV PADHI</style></author><author><style face="normal" font="default" size="100%">P.D.N. SRINIVASU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">CONDITIONS FOR EXISTENCE OF POSITIVE SOLUTIONS OF FIRST ORDER BOUNDARY VALUE PROBLEMS WITH DELAY AND NONLINEAR NONLOCAL BOUNDARY CONDITIONS AND APPLICATION TO HEMATOPOIESIS</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%">CAA</style></alt-title><short-title><style face="normal" font="default" size="100%">Existence of Positive Solutions</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B08</style></keyword><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></keywords><dates><year><style  face="normal" font="default" size="100%">2017</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%">http://www.acadsol.eu/en/articles/21/1/4.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%">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, &amp;nbsp;existence criteria for &amp;nbsp; positive solutions of the following nonlinear first order boundary value problem with delay and &amp;nbsp;nonlinear nonlocal boundary condition&lt;br /&gt;
&amp;nbsp;\begin{eqnarray*}&lt;br /&gt;
&amp;nbsp;x^{\prime}(t) &amp;amp; = &amp;amp; r(t)x(t) + p(t) \sum_{i=1}^{m} f_i(t,x(\alpha_{i}(t))), \,\,\, t \in [0,1],\\&lt;br /&gt;
&amp;nbsp;\lambda x(0) &amp;amp; = &amp;amp; x(1) + \sum_{j=1}^{n} \Lambda_j(\tau_j, x(\tau_j)),\,\,\, \tau_j \in [0,1],&lt;br /&gt;
&amp;nbsp;\end{eqnarray*}&lt;br /&gt;
&amp;nbsp;are established using &amp;nbsp;Leray-Schauder theorem and Leggett-Williams fixed point theorem. These results are employed to &amp;nbsp;provide a complete existence criteria for positive solutions of the following &amp;nbsp;boundary value problem associated with the well known Hematopoiesis &amp;nbsp;model%\vfill\mbox{}\newpage&lt;br /&gt;
&amp;nbsp;\begin{align}&lt;br /&gt;
&amp;nbsp;x^{\prime}(t) &amp;nbsp;= &amp;amp; r(t)x(t) + p(t)\frac{x^{n}(t-\alpha)}{1+x^{m}(t-\alpha)}, \,\,\, t \in [0,1], \nonumber\\&lt;br /&gt;
&amp;nbsp; \lambda x(0) &amp;nbsp; = &amp;amp; &amp;nbsp;x(1) &amp;nbsp;+ &amp;nbsp;\Lambda(\tau,x(\tau)),\,\,\, \tau \in [0,1] \nonumber&lt;br /&gt;
&amp;nbsp;\end{align}&lt;br /&gt;
&amp;nbsp;where $m$ and $n$ are nonnegative parameters.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><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%">John R. Graef</style></author><author><style face="normal" font="default" size="100%">LINGJU KONG</style></author><author><style face="normal" font="default" size="100%">MIN WANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">TWO NONTRIVIAL SOLUTIONS FOR A DISCRETE FOURTH ORDER PERIODIC BOUNDARY VALUE PROBLEM</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B08</style></keyword><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">58E3</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/19/4/1.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;We study the discrete fourth order periodic boundary value problem with a parameter $${ \left\{ \begin{array}{1}∆^4u(t − 2) − ∆ \left(p(t − 1)∆_u(t − 1)\right)&amp;nbsp;+ q(t)u(t) = λf(t, u(t)), \ t ∈ [1, N]_Z,\\&amp;nbsp;∆^iu(−1) = ∆^iu(N − 1), \ \&amp;nbsp; &amp;nbsp;i = 0, 1, 2, 3.\end{array}\right. }$$ By using variational methods and the mountain pass lemma, sufficient conditions are found under which the above problem has at least two nontrivial solutions. One example is included to illustrate the result.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><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%">ANDREW CONNER</style></author><author><style face="normal" font="default" size="100%">MIN WANG</style></author><author><style face="normal" font="default" size="100%">CLAIRE ZAJACZKOWSKI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">UNIQUENESS AND PARAMETER DEPENDENCE OF POSITIVE SOLUTIONS OF DISCRETE PERIODIC BOUNDARY VALUE PROBLEMS</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B08</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%">http://www.acadsol.eu/en/articles/19/2/1.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 class=&quot;rtejustify&quot;&gt;The authors study a type of second order nonlinear discrete periodic boundary value problems. The existence and uniqueness of positive solutions are discussed. The parametric dependence of the solutions is also investigated. Two examples are given as applications of 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%">163</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">FRANCOIS GENOUD</style></author><author><style face="normal" font="default" size="100%">BRYAN P. RYNNE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOME RECENT RESULTS ON THE SPECTRUM OF MULTI-POINT EIGENVALUE PROBLEMS FOR THE p-LAPLACIAN</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B08</style></keyword><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">34L05</style></keyword><keyword><style  face="normal" font="default" size="100%">47J15</style></keyword><keyword><style  face="normal" font="default" size="100%">47N20</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%">http://www.acadsol.eu/en/articles/15/4/1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">15</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 describe some recent results regarding the spectral properties of &lt;em&gt;p&lt;/em&gt;-Laplacian problems subject to various forms of multi-point boundary conditions. In particular, we consider Dirichlet and Neumann-type boundary conditions, and mixtures of these conditions. We also consider certain types of nonlocal boundary conditions expressed in terms of Stieltjes integrals, which have been discussed recently and which generalize the previously considered multi-point conditions. It is shown that, under suitable assumptions, the structure of the spectrum and the properties of the eigenfunctions for these boundary value problems with nonlocal boundary conditions are very similar to those of the classical linear Sturm-Liouville problem with separated boundary conditions. Results on global bifurcation, non-resonance conditions and existence of nodal solutions for related nonlinear problems are also presented. In a final section we discuss the necessity of some of the hypotheses we impose, and outline some open problems.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">413</style></section></record></records></xml>