On the Existence of Positive Periodic Solutions for Neutral Functional Differential Equation with Multiple Deviating Arguments

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• 作者：Shi-ping Lu ^A1 and Wei-gao Ge ^A2
• 关键词：Positive periodic solution ; k-set contraction ; coincidence degree ; neutral functional differential equation
• 刊名：Acta Mathematicae Applicatae Sinica (English Series)
• 出版年：2003
• 出版时间：November 2003
• 年：2003
• 卷：19
• 期：4
• 页码：631-640
• 全文大小：203 KB

文摘

By means of an abstract continuation theory for k-set contraction and continuation theorem of coincidence degree principle, some criteria are established for the existence of positive periodic solutions of following neutral functional differential equation % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaada % WcaaqaaiaadsgacaWGobaabaGaamizaiaadshaaaGaaGjcVlabg2da % 9iaayIW7caWGobWaaeWaaeaacaWG0baacaGLOaGaayzkaaWaamWaae % aacaWGHbWaaeWaaeaacaWG0baacaGLOaGaayzkaaGaeyOeI0IaeqOS % di2aaeWaaeaacaWG0baacaGLOaGaayzkaaGaamOtamaabmaabaGaam % iDaaGaayjkaiaawMcaaiabgkHiTmaaqahabaGaamOyamaaBaaaleaa % caWGQbaabeaakmaabmaabaGaamiDaaGaayjkaiaawMcaaiaad6eada % qadaqaaiaadshacqGHsislcqaHdpWCdaWgaaWcbaGaamOAaaqabaGc % daqadaqaaiaadshaaiaawIcacaGLPaaaaiaawIcacaGLPaaacqGHsi % sldaaeWbqaaiaadogadaWgaaWcbaGaamyAaaqabaGcdaqadaqaaiaa % dshaaiaawIcacaGLPaaaceWGobGbauaaaSqaaiaadMgacqGH9aqpca % aIXaaabaGaamyBaaqdcqGHris5aOWaaeWaaeaacaWG0bGaeyOeI0Ia % eqiXdq3aaSbaaSqaaiaadMgaaeqaaOWaaeWaaeaacaWG0baacaGLOa % GaayzkaaaacaGLOaGaayzkaaaaleaacaWGQbGaeyypa0JaaGymaaqa % aiaad6gaa0GaeyyeIuoaaOGaay5waiaaw2faaiaac6caaaa!7C35! $$ \frac{{dN}} {{dt}}{\kern 1pt} = {\kern 1pt} N{\left( t \right)}{\left[ {a{\left( t \right)} - \beta {\left( t \right)}N{\left( t \right)} - {\sum\limits_{j = 1}^n {b_{j} {\left( t \right)}N{\left( {t - \sigma _{j} {\left( t \right)}} \right)} - {\sum\limits_{i = 1}^m {c_{i} {\left( t \right)}{N}'} }{\left( {t - \tau _{i} {\left( t \right)}} \right)}} }} \right]}. $$