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

Abstract

In this paper, the 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 Holder's inequality, stochastic analysis, fixed point strategy and the theory of strongly continuous cosine families with the Hausdorff measure of noncompactness, a new set of sufficient conditions is formulated
which guarantees the asymptotic behavior of the nonlinear second-order stochastic system. The results are obtained under the assumption that the conditions which are different from Lipschitz
conditions in the literature. An example is also discussed to illustrate the efficiency of the obtained results.