Existence and uniqueness of solutions for neutral periodic integro-diferential equations with infnite delay

Abstract

We prove the existence of solutions for the neutral periodic integro-diferential equation with infnite delay x 0 ( t) = G(t, x(t), x(t − τ (t))) + d dt Q(t, x(t − τ (t))) + Z t −∞ Xn j=1 gj (t, s)

x(t + T) = x(t). A Krasnoselskii and Banach’s fxed point theorems are employed in establishing our results