Asmptotic behavior of a class of impulsive partial stochastic functional neutral integrodifferential equations with infinite delay

Abstract

This paper is devoted to the existence and asymptotic behavior in p-th moment of the mild solution to a class of impulsive neutral stochastic functional integro- differential equations with infinite delay in Hilbert spaces. A new and sufficient set of conditions are formulated concerning the existence of solutions and the stability. of the nonlinear stochastic system. To obtain the desired result, the theory of the resolvent operator in the sense of Grimmer, the stochastic analysis theory, the fixed point theorem and the Hausdorff measure of non-compactness are used. However, it is very important to specify that in this paper, we have left the classical framework in which the nonlinear terms are assumed to be Lipschitz continuous. At the end of this paper, an illustration is also given to show the application of our results.