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 formddtx(t)=A(t)x(t)+ddtQ(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)yy′=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.