  In this paper, we are devoted to consider the periodic problem for the
impulsive evolution equations with delay in Banach space. By using operator
semigroups theory and 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 $\omega$-periodic mild solution.
