Asymptotic Stability of Stochastic Impulsive Neutral Partial Functional Differential Equations

Abstract

In this paper the authors study the existence and asymptotic stability in p-th moment of mild solutions to stochastic neutral partial differential equation with impulses. Their method for investigating the stability of solutions is based on the fixed point theorem.

A note on controllability of impulsive neutral stochastic functional differential equations driven by a Rosenblatt process in a Hilbert space

“…Recently, there has been increasing interest in the analysis and synthesis of impulsive systems due to their significance both in theory and applications. Thus the theory of impulsive differential equations has seen considerable development (see [1,12,5,18] and references therein).…”

Asymptotic behaviour of mild solution of nonlinear stochastic partial functional equations

“…Neutral stochastic differential equations with delays are often used to describe such systems (see, e.g., [19,30]). On the other hand, the stability of impulsive differential equations has been discussed by several authors (see, e.g., [2,10,26,32,33,38]).…”

Existence and Stability for Stochastic Impulsive Neutral Partial Differential Equations Driven by Rosenblatt Process with Delay and Poisson Jumps

“…On the other hand, the stability of impulsive differential equations has been discussed by several authors (see, e.g. [1,18,23,27]). In addition, the study of neutral SFDEs driven by jumps process also have begun to gain attention and strong growth in recent years.…”