On the Existence and Stability of Periodic Solutions for a Nonlinear Neutral Functional Differential Equation

Abstract

This paper deals with the existence and stability of periodic solutions for the following nonlinear neutral functional differential equation $\mathrm{(d}/d\mathrm{t)}D{u}_t=p(t)-au(t)-aqu(t-r)-h(u(t),u(t-r)).$ By using Schauder-fixed-point theorem and Krasnoselskii-fixed-point theorem, some sufficient conditions are obtained for the existence of asymptotic periodic solutions. Main results in this paper extend the related results due to Ding (2010) and Lopes (1976).