Existence and stability of mild solutions to parabolic stochastic partial differential equations driven by Levy space-time noise

This paper is concerned with the well-posedness and stability of parabolic stochastic partial differential equations. Firstly, we obtain some sufficient conditions ensuring the existence and uniqueness of mild solutions, and some H-stability criteria for a class of parabolic stochastic partial differential equations driven by Levy space-time noise under the local/non-Lipschitz condition. Secondly, we establish some existence-uniqueness theorems and present sufficient conditions ensuring the H'-stability of mild solutions for a class of parabolic stochastic partial functional differential equations driven by Levy space-time noise under the local/non-Lipschitz condition. These theoretical results generalize and improve some existing results. Finally, two examples are given to illustrate the effectiveness of our main results.