Existence and mean-square exponential stability of mild solutions for impulsive stochastic partial differential equations with noncompact semigroup

Abstract

In this paper, with the help of the Hausdorff measure of noncompactness, the Mönch fixed point theorem and some inequality technique, some new criteria to guarantee the mild solution for impulsive stochastic partial differential equations with varying-time delays are obtained. Then, by establishing a new impulsive-integral inequality, some sufficient conditions to ensure mean-square exponential stability of mild solution for impulsive stochastic partial differential equations with varying-time delays are obtained which will significantly improve some previous results [5,20]. At last, we give an example to illustrate the effectiveness and feasibility of the obtain results in our paper.