<?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%">BARUCH CAHLON</style></author><author><style face="normal" font="default" size="100%">DARRELL SCHMIDT</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NECESSARY CONDITIONS AND ALGORITHMIC STABILITY TESTS FOR CERTAIN HIGHER ODD ORDER NEUTRAL DELAY DIFFERENTIAL EQUATIONS</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%">asymptotic stability</style></keyword><keyword><style  face="normal" font="default" size="100%">characteristic functions</style></keyword><keyword><style  face="normal" font="default" size="100%">delay</style></keyword><keyword><style  face="normal" font="default" size="100%">necessary conditions</style></keyword><keyword><style  face="normal" font="default" size="100%">stability criteria</style></keyword><keyword><style  face="normal" font="default" size="100%">stability regions</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/16-DSA-31-12.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">23</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 obtain necessary conditions and robust algorithmic criteria for asymptotic stability of the zero solution of higher odd order linear neutral delay differential equations of the form y (2m+1)(t) + αy(2m+1)(t − τ) = X 2m j=0 ajy (j) (t) +X 2m j=0 bjy (j) (t − τ) where aj , bj, and α 6=&amp;nbsp;0 are real constants. Here τ &amp;gt; 0 is a constant delay. In proving our results we make use of Pontryagin’s theory for quasi-polynomials.&lt;/p&gt;
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