pTH Moment Exponential Stability of Stochastic Partial Differential Equations with Poisson Jumps

ABSTRACT In this paper, we study a class of stochastic partial differential equations with Poisson jumps, which is more realistic for establishing mathematical models since it has been widely applied in many fields. Under a reasonable condition, we not only establish the existence and uniqueness of the mild solution for the investigated system but also prove that it is p th moment exponentially stable by using the fixed point theory. Then, based on the well‐known Borel‐Cantelli lemma, further, we prove that the mild solution is almost surely p th moment exponentially stable. Our results improve and generalize those given in the previous literature, in particular, the Lyapunov direct method and successive approximation method. Finally, we give an example to illustrate the effectiveness of the obtained results.