Existence and uniqueness of periodic solutions for a system of nonlinear neutral functional differential equations with two functional delays

Abstract

In this paper, we study the existence of periodic solutions of the nonlinear neutral system of differential equations $$\begin{aligned} \frac{d}{dt}x\left( t\right) =A\left( t\right) x\left( t-\tau \left( t\right) \right) +\frac{d}{dt}Q\left( t,x\left( t-g\left( t\right) \right) \right) +G\left( t,x\left( t\right) ,x\left( t-g\left( t\right) \right) \right) \!. \end{aligned}$$ By using Krasnoselskii’s fixed point theorem we obtain the existence of periodic solution and by contraction mapping principle we obtain the uniqueness. Our results extend and complement some earlier publications.