Poisson stable solutions for stochastic PDEs driven by Levy noise

This paper is mainly concerned with the existence, uniqueness and Poisson stability (including station-arity, periodicity, almost periodicity and almost automorphy) of solutions for a class of stochastic partial differential equations driven by Levy noise, where the involved coefficients are assumed to be strictly mono-tone. Based on the variational method, we establish the well-posedness of L-2-bounded solution and then prove that it has the same characters of periodicity, almost periodicity and almost automorphy as the co-efficients of the equation. Moreover, we also investigate the additive noise case under strong monotone condition. In particular, we illustrate our results by applying to concrete models such as stochastic reaction-diffusion equations, stochastic porous media equations and stochastic p-Laplace equations. (c) 2023 Elsevier Inc. All rights reserved.