<?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%">U.A. ABASIEKWERE</style></author><author><style face="normal" font="default" size="100%">I.M. ESUABANA</style></author><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%">EXISTENCE THEOREM FOR LINEAR NEUTRAL IMPULSIVE DIFFERENTIAL EQUATIONS OF THE SECOND ORDER</style></title><secondary-title><style face="normal" font="default" size="100%">LINEAR NEUTRAL IMPULSIVE EQUATIONS</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><keyword><style  face="normal" font="default" size="100%">34K45</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/en/articles/22/2/1.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><isbn><style face="normal" font="default" size="100%">1083-2564</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, we consider the second order linear neutral&amp;nbsp;impulsive differential equation of the form&lt;/p&gt;

&lt;p class=&quot;rtecenter&quot;&gt;$$ \left\{\begin{array}{ll} \left[y\left(t\right)- p y\left(t-\tau \right)\right]^{{''} } + q\left(t\right)y\left(g\left(t\right)\right) = 0, &amp;amp;\quad t\ne t_{k},\\ \Delta \left[y\left(t_{k} \right)- p y\left(t_{k} -\tau \right)\right]^{{'} } + q_{k} y\left(g\left(t_{k} \right)\right) = 0, &amp;amp;\quad \forall t=t_{k} , \end{array}\right. $$&lt;/p&gt;

&lt;p&gt;where $p\in R$, $ q_{k} \ge 0$, $ q \in P C \left(\left[t_{0} ,\infty \right), R_{+} \right)$, $ g\in C\left(\left[t_{0} ,\infty \right), R\right)$, $ \mathop{\lim }\limits_{t\to \infty } g \left(t\right)= \infty ,$ $\tau &amp;gt;0.$&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;We establish conditions for the existence of a positive solution with asymptotic decay by defining a map which satisfies the assumptions of Krasnoselkii’s fixed point theorem.&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%">135</style></section></record></records></xml>