Periodic solutions and stability in a nonlinear neutral system of differential equations with infinite delay

In this paper, we study the existence of periodic solutions of the nonlinear neutral system of differential equations d d t x t = A t x t + d d t Q t , x t - g t + ∫ - ∞ t D t , s F x s d s . Using Krasnoselskii’s fixed point theorem, we obtain the existence of periodic solution and by contraction mapping principle we obtain the uniqueness of periodic solution and stability of the zero solution. Our results extend some earlier publications.