Existence and Stability Results for Time-Dependent Impulsive Neutral Stochastic Partial Integrodifferential Equations with Rosenblatt Process and Poisson Jumps

Abstract

In this paper, we discuss the existence, uniqueness and stability of mild solutions of time-dependent impulsive neutral stochastic partial integrodifferential equations with the Rosenblatt process and Poisson jumps. The existence of mild solutions for the equations is discussed by means of the semigroup theory and theory of the resolvent operator. Next, under some sufficient conditions, the results are obtained by using the method of successive approximation and Bihari’s inequality. Finally, an example is provided to illustrate our results.