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

Abstract

In this study, we employ the fixed point theorem of Krasnoselskii andthe concepts of separate and large contractions to show the existenceof a periodic solution of a highly nonlinear delay differential equation.Also, we give a classification theorem providing sufficient conditions foran operator to be a large contraction, and hence, a separate contraction.Finally, under slightly different conditions, we obtain the existence ofa positive periodic solution.