Piecewise asymptotically almost periodic solution of neutral Volterra integro-differential equations with impulsive effects

In this paper, we investigate the existence and uniqueness of a piecewise asymptotically almost periodic mild solution to nonautonomous neutral Volterra integro-differential equations with impulsive effects in Banach space. The working tools are based on the Krasnoselskii's fixed point theorem and semigroup theory. In order to illustrate our main results, we study the piecewise asymptotically almost periodic solution of the impulsive partial differential equations with Dirichlet conditions.