Periodic solutions of neutral nonlinear system of differential equations with functional delay

We study the existence of periodic solutions of the nonlinear neutral system of differential equations of the form d dt x(t) = A(t)x(t)+ d dt Q t,x t − g(t) +G t,x(t),x t −g(t) . In the process we use the fundamental matrix solution of y = A(t)y and convert the given neutral differential equation into an equivalent integral equation. Then we construct appropriate mappings and employ Krasnoselskii’s fixed point theorem to show the existence of a periodic solution of this neutral differential equation. We also use the contraction mapping principle to show the existence of a unique periodic solution of the equation. © 2006 Elsevier Inc. All rights reserved