Existence and stability of almost periodic solutions to impulsive stochastic differential evolution equations with infinite delay

TL;DR

This paper establishes conditions for the existence and stability of almost periodic solutions in impulsive stochastic differential equations with infinite delay, advancing understanding of their long-term behavior in Banach spaces.

Contribution

It introduces new sufficient conditions for existence and exponential stability of almost periodic solutions in impulsive stochastic differential equations with infinite delay.

Findings

Existence of square mean piecewise almost periodic solutions is proven.

Conditions for exponential stability of these solutions are derived.

The results apply to equations in Banach spaces with impulsive effects and infinite delay.

Abstract

In this paper, we investigate a class of nonlinear impulsive stochastic differential evolution equations with infinite delay in Banach space. Based on the Krasnoselskii's fixed point theorem, sufficient conditions of the existence of the square mean piecewise almost periodic solutions to this type of equations are derived. Moreover, the exponential stability of the square mean piecewise almost periodic solution is investigated.