Exponential behavior of nonlinear stochastic partial functional equations driven by Poisson jumps and Rosenblatt process

Abstract

In this article, we discuss the Asymptotic behaviour of mild solutions of nonlinear stochastic partial functional equations driven by Poisson jumps and Rosenblatt process. The Banach fixed point theorem and the theory of resolvent operator devolped by Grimmer are used. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained results.