The existence and uniqueness of periodic solutions for nonlinear neutral dynamic equation with infinite delay on a Time Scale.

Abstract

Let   be a periodic time scale. We study the following nonlinear neutral dynamic equation with infinite delay
by using a fixed point theorem due to Krasnoselskii, we show that the nonlinear neutral dynamic equation with an infinite delay has a periodic solution. In addition, through utilizing the contraction mapping principle, we have shown that this periodic solution is unique.