Periodic solutions for a second order nonlinear neutral functional differential equation with variable delay

Abstract

In this paper we study the existence of periodic solutions of the second order nonlinear neutral differential equation with functional delay. We invert the given equation to obtain an integral, but equivalent, equation from which we define a fixed point mapping written as a sum of a large contraction and a compact map. We show that, under suitable conditions, such maps fit very nicely into the framework of Krasnoselskii-Burton's fixed point theorem so that the existence of periodic solutions is concluded.

Keywords

• Periodic solutions
• Nonlinear neutral differential equations
• large contraction