Periodic Solutions for Impulsive Neutral Dynamic Equations with Infinite Delay on Time Scales

A. Ardjouni, A. Djoudi

Let $\mathbb{T}$ be a periodic time scale. We use the Krasnoselskii's fixed point theorem to show that the impulsive neutral dynamic equations with infinite delay \begin{align*} x^{\Delta}(t)&=-A(t)x^{igma}(t)+g^{\Delta}(t,x(t-h(t)))+ıt_{-ıfty}^{t}Deft( t,u\right) f(x(u))riangle u, \quad teq t_{j}, tı\mathbb{T}, x(t_{j}^{+})&=x(t_{j}^{-})+I_{j}(x(t_{j})),\quad jı\mathbb{Z}^{+}\end{align*} have a periodic solution. Under a slightly more stringent conditions we show that the periodic solution is unique using the contraction mapping principle.