<?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%">S.H. SAKER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OSCILLATION OF SECOND-ORDER DELAY AND NEUTRAL DELAY DYNAMIC EQUATIONS ON TIME SCALES</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%">34A99</style></keyword><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">34K11</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A11</style></keyword><keyword><style  face="normal" font="default" size="100%">39A99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/345-360-DSA-26-18-Saker.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">15</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, we consider the second-order linear delay dynamic equation x ∆∆(t) + q(t)x(τ (t)) = 0, on a time scale T. We will study the properties of the solutions and establish some sufficient conditions for oscillations. In the special case when T = R and τ (t) = t, our results include some well-known results in the literature for differential equations. When, T = Z, T = hZ, for h &amp;gt; 0 and T = Tn = {tn : n ∈ N0} where tn} is the set of the harmonic numbers defined by t0 = 0, tn = Pn k=1 1 k for n ∈ N0 our results are essentially new. The results will be applied on second-order neutral delay dynamic equations in time scales to obtain some sufficient conditions for oscillations. An example is considered to illustrate the main results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">345</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%">DAQING JIANG</style></author><author><style face="normal" font="default" size="100%">P. Y. H. PANG</style></author><author><style face="normal" font="default" size="100%">RAVI AGARWAL</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">UPPER AND LOWER SOLUTIONS METHOD AND A SUPERLINEAR SINGULAR DISCRETE BOUNDARY VALUE PROBLEM</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%">34B16</style></keyword><keyword><style  face="normal" font="default" size="100%">39A99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/743-754-Ravi-05.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</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&gt;In this paper, we study the singular discrete boundary value problem    ∆[φ(∆u(t − 1))] + g(t, u(t)) = 0, t ∈ {1, 2, . . . , T}, u(0) = u(T + 1) = 0 where φ(s) = |s| p−2 s, p &amp;gt; 1, and the function g is superlinear at infinity and may change sign or be singular at u = 0. Existence of solutions is obtained via an upper and lower solutions method.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">743</style></section></record></records></xml>