Weighted pseudo almost automorphic solutions for nonautonomous SPDEs driven by Lévy noise

In this paper, we introduce the concept of weighted pseudo almost automorphy in distribution. Using the theory of evolution family and stochastic analysis method, we establish the existence and uniqueness results of almost automorphic solutions in distribution and weighted pseudo almost automorphic solutions in distribution for some semilinear nonautonomous stochastic partial differential equations driven by Lévy noise, when the coefficients of the equations satisfy some suitable conditions. Moreover, we investigate the global exponentially stability of these solutions. The results are generalizations of the results in Wang and Liu [32], Chen and Lin [11] and Liu and Sun [26].