The Existence and Uniqueness of Periodic Solutions for Nonlinear Neutral first order differential equation with Functional Delay

Abstract

This paper is devoted to employ the fixed point theorem of Krasnoselskii, to show the existence and uniqueness of periodic solutions of the nonlinear neutral differential equation
By modifying the given neutral differential equation into an equivalent integral equation using lemma (2.1). This is done by creating a suitable operators, one is a compact and the other is contraction , which allow us to prove the existence of periodic solutions. Also, we used the Banach fixed point theorem to guarantee a unique periodic solution.