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

Abstract

We study the existence of periodic solutions of the nonlinear neutral system of differential equations of the formfrac(d, d t) x (t) = A (t) x (t) + frac(d, d t) Q (t, x (t - g (t))) + G (t, x (t), x (t - g (t))) . In the process we use the fundamental matrix solution ofy′ = 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.