Existence and asymptotic stability of periodic solutions for impulsive delay evolution equations

This paper we devote to considering the periodic problem for the impulsive evolution equations with delay in Banach space. By using operator semigroup theory and the fixed point theorem, we establish some new existence theorems of periodic mild solutions for the equations. In addition, with the aid of an integral inequality with impulsive and delay, we present essential conditions on the nonlinear and impulse functions to guarantee that the equations have an asymptotically stable ω -periodic mild solution.