Asymptotic Behavior of Second-Order Impulsive Partial Stochastic Functional Neutral Integrodifferential Equations with Infinite Delay

Abstract

In this paper, the existence and asymptotic stability in p-th moment of mild solutions to a class of second-order impulsive partial stochastic functional neutral integrodifferential equations with infinite delay in Hilbert spaces is considered. By using Hölder’s inequality, stochastic analysis, fixed point strategy and the theory of strongly continuous cosine families with the Hausdor measure of noncompactness, a new set of sufficient conditions is formulated which guarantees the asymptotic behavior of the nonlinear second-order stochastic system. These conditions do not require the the nonlinear terms are assumed to be Lipschitz continuous. An example is also discussed to illustrate the efficiency of the obtained results.