Asymptotic stability of neutral stochastic functional integro-differential equations with impulses

Abstract

This paper is concerned with the existence and asymptotic stability in the \,p-th moment of mild solutions of nonlinear impulsive stochastic delay neutral partial functional integro-differential equations. We suppose that the linear part possesses a resolvent operator in the sense given by Grimmer 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 theory developed in this work.