SEPARATE CONTRACTION AND EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR DELAY DIFFERENTIAL EQUATIONS

Authors : Murat ADIVAR, Muhammad N. ISLAM, Youssef N. RAFFOUL

Pages : 1-13

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Publication Date : 2012-01-01

Article Type : Research Paper

Abstract :In this study, we employ the fixed point theorem of Krasnoselskii and the concepts of separate and large contractions to show the existence of a periodic solution of a highly nonlinear delay differential equation. Also, we give a classification theorem providing sufficient conditions for an operator to be a large contraction, and hence, a separate contraction. Finally, under slightly different conditions, we obtain the existence of a positive periodic solution.
Keywords : Krasnoselskiis fixed point theorem, Large contraction, Periodic solution, Positive periodic solution, Separate contraction, Totally nonlinear delay differential equations