Periodicity of Solutions for Non-Autonomous Neutral Functional Differential Equations with State-Dependent Delay

This paper is concerned with the existence of solutions and periodic solutions for a class of semilinear neutral functional differential equations with state-dependent delay, in which the linear part is non-autonomous and generates a linear evolution operator. We first establish the existence and regularity of bounded solutions for the considered equation, and then we show by using Banach fixed point theorem that these solutions have periodicity property or asymptotic periodicity property respectively under some conditions . Finally, an example to illustrate the obtained results is given.