Asymptotic behavior, attracting and quasi-invariant sets for impulsive neutral SPFDE driven by Lévy noise

Abstract

By establishing two new impulsive-integral inequalities, the attracting and quasi-invariant sets of the mild solution for impulsive neutral stochastic partial functional differential equations driven by Lévy noise are obtained, respectively. Moreover, we shall derive some sufficient conditions to ensure stability of this mild solution in the sense of both moment exponential stability and almost surely exponential stability.