Fixed points and exponential stability for stochastic partial integro–differential equations with delays

Abstract

In this paper, we study the existence and asymptotic stability in the pth-moment of mild solutions of nonlinear impulsive stochastic partial functional integro-differential equations with delays. We suppose that the linear part possesses a resolvent operator in the sense given by Grimmer in [9] , and the nonlinear terms are assumed to be Lipschitz continuous. A fixed point approach is used to achieve the required result. An example is provided to illustrate the abstract results in this work.