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

Year 2012, Volume: 41 Issue: 1, 1 - 13, 01.01.2012

Murat Adıvar Muhammad N. Islam Youssef N. Raffoul

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

Krasnoselskii’s fixed point theorem, Large contraction, Periodic solution, Positive periodic solution, Separate contraction, Totally nonlinear delay differential equations

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

Abstract

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