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

Abstract

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 ω-periodic mild solution.

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“…As we all know, the existence, uniqueness, and stability of periodic solutions of differential equations have always been an important research hotspot in the field of differential equations (see [10][11][12][13][14][15][16][17][18][19][20]). However, the above literatures are basically about the study of periodic solutions of specific equations, rather than the study of general differential equations.…”

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