THE EXISTENCE AND EXPONENTIAL STABILITY FOR NEUTRAL STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY AND POISSON JUMP

摘要

In this paper, the problems on the existence and uniqueness, the exponential stability in mean square for mild solution of neutral stochastic partial differential equations with infinite delay and Poisson jump are considered. Firstly, the existence and uniqueness for mild solution of such systems is studied by using the Banach fixed point theorem. Then, by establishing an integral inequality, the exponential stability in mean square for mild solution to neutral stochastic partial differential equations with infinite delay and Poisson jump is discussed. Compared with the previous works, our method is new and our results can generalize and improve some existing results. Finally, an example is given to show the effectiveness of the obtained results.