Existence and exponential stability of the piecewise pseudo almost periodic mild solution for some partial impulsive stochastic neutral evolution equations

Abstract

In the present paper, we first introduce the concept of double measure ‐mean piecewise pseudo almost periodic for stochastic processes for . Next, we make extensive use of the exponential dichotomy techniques and a fixed point strategy with stochastic analysis theory to obtain the existence of doubly measure ‐mean piecewise pseudo almost periodic mild solutions for a class of impulsive non‐autonomous partial stochastic evolution equations in Hilbert spaces. In addition, we study the exponential stability of ‐mean piecewise pseudo almost periodic mild solutions. Finally, we give an example to confirm the reliability and feasibility of our findings.