<?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%">SESHADEV PADHI</style></author><author><style face="normal" font="default" size="100%">SMITA PATI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MULTIPLE POSITIVE PERIODIC SOLUTIONS FOR A NONLINEAR FIRST ORDER FUNCTIONAL DIFFERENCE EQUATION WITH APPLICATION TO HEMATOPOIESIS MODEL</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K13</style></keyword><keyword><style  face="normal" font="default" size="100%">34K15</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%">http://www.acadsol.eu/en/articles/19/3/1.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;Sufficient conditions are obtained for the existence of at least three positive &lt;em&gt;T&lt;/em&gt; - periodic solutions for the first order functional difference equation $$ { ∆x(n) = −a(n)x(n) + f(n, x(h(n))). }$$ The Leggett-Williams multiple fixed point theorem has been used to prove our results. We have applied our results to Hematopoiesis models in population dynamics and obtained an interesting result. The result is new in the literature.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</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%">SESHADEV PADHI</style></author><author><style face="normal" font="default" size="100%">SHILPEE SRIVASTAVA</style></author><author><style face="normal" font="default" size="100%">SMITA PATI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">POSITIVE PERIODIC SOLUTIONS FOR FIRST ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Applied Analysis</style></secondary-title><short-title><style face="normal" font="default" size="100%">POSITIVE PERIODIC SOLUTIONS</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">34C27</style></keyword><keyword><style  face="normal" font="default" size="100%">34K13</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%">12/2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/14/4/3.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">14</style></volume><pages><style face="normal" font="default" size="100%">462</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;div class=&quot;rtejustify&quot;&gt;We establish conditions for the existence of at least two positive periodic solutions of the following functional differential equation of the form&lt;/div&gt;

&lt;div class=&quot;rtecenter&quot;&gt;&lt;img alt=&quot;&quot; height=&quot;32&quot; src=&quot;data:image/png;base64,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&quot; width=&quot;210&quot; /&gt;&lt;/div&gt;

&lt;div class=&quot;rtejustify&quot;&gt;Applications to some ecological models are given.&lt;/div&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><section><style face="normal" font="default" size="100%">447</style></section></record></records></xml>