Study of the Periodic or Nonnegative Periodic Solutions of Functional Differential Equations via Krasnoselskii–Burton’s Theorem

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• 作者：Mouataz Billah Mesmouli…
• 关键词：Krasnoselskii–Burton’s theorem ; Large contraction ; Neutral differential equation ; Integral equation ; Periodic solution ; Nonnegative solution
• 刊名：Differential Equations and Dynamical Systems
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：24
• 期：4
• 页码：391-406
• 全文大小：439 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  
• 出版者：Springer India
• ISSN：0974-6870
• 卷排序：24

文摘

In this paper, we study the existence of periodic or nonnegative periodic solutions of the nonlinear neutral differential equation $$\begin{aligned} \frac{\mathrm{d}}{\mathrm{d}t}[x(t)-Q(t,\,x(t-\tau (t)))]=-a(t)h(x(t-\tau (t))) +G(t,\,x(t),\,x(t-\tau (t))). \end{aligned}$$We invert this equation to construct a sum of a compact map and a large contraction which is suitable for applying the modification of Krasnoselskii’s theorem. The Caratheodory condition is used for the functions Q and G.KeywordsKrasnoselskii–Burton’s theoremLarge contractionNeutral differential equationIntegral equationPeriodic solutionNonnegative solutionMathematics Subject Classification34K4035B0935B1045J05References1.Adıvar, M., Islam, M.N., Raffoul, Y.N.: Separate contraction and existence of periodic solution in totally nonlinear delay differential equations. Hacet. J. Math. 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Nonlinear Anal. 63, e233–e242 (2005)MATHCrossRefGoogle ScholarCopyright information© Foundation for Scientific Research and Technological Innovation 2015Authors and AffiliationsMouataz Billah Mesmouli1Abdelouaheb Ardjouni12Email authorAhcene Djoudi11.Applied Mathematics Lab., Department of Mathematics, Faculty of SciencesUniv AnnabaAnnabaAlgeria2.Department of Mathematics and InformaticsUniv Souk AhrasSouk AhrasAlgeria About this article CrossMark Print ISSN 0971-3514 Online ISSN 0974-6870 Publisher Name Springer India About this journal Reprints and Permissions Article actions Export citation .RIS Papers Reference Manager RefWorks Zotero .ENW EndNote .BIB BibTeX JabRef Mendeley Share article Email Facebook Twitter LinkedIn Cookies We use cookies to improve your experience with our site. More information Accept Over 10 million scientific documents at your fingertips