<?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%">SAMUEL CASTILLO</style></author><author><style face="normal" font="default" size="100%">MANUEL PINTO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ASYMPTOTIC BEHAVIOR OF FUNCTIONAL DYNAMIC EQUATIONS IN TIME SCALE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</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%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/12-DSA-229.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%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;It is considered a scalar linear functional dynamic equation in time scale with delayed argument of the form&lt;/p&gt;

&lt;p&gt;(0.1)&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;y&lt;sup&gt;∆&lt;/sup&gt;(t) = b(t) y( τ(t) ), t ∈ T ∩ [0, +∞]&lt;/p&gt;

&lt;p&gt;where T, the time scale, is a closed subset of R without upper bound for this case,&lt;sup&gt; ∆&lt;/sup&gt; is de Hilger’s derivate, which among other things, unifies difference operator for sequences and the derivate. The functions b, τ : T → C, τ &amp;gt; 0, are “locally integrable” and satisfy integral smallness conditions in a sense to be defined later. Asymptotic formulas of solutions of equation (0.1) are given. They unify and extend asymptotic formulas of difference and differential equations.&lt;/p&gt;
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