<?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></records></xml>