Exponential Stable Behavior of a Class of Impulsive Partial Stochastic Differential Equations Driven by Lévy Noise

Abstract

In this paper, using exponential stable property, the stochastic analysis techniques and a fixed-point theorem for condensing maps, we obtain the existence results of piecewise weighted pseudo almost periodic in distribution mild solutions for a class of impulsive partial stochastic differential equations driven by Lévy noise in Hilbert spaces under non-Lipschitz conditions. Furthermore, the exponential stable of mild solution in mean square is investigated. Finally, an example is presented to illustrate the results.