On Almost Automorphic Mild Solutions for Nonautonomous Stochastic Evolution Equations

Abstract EN

We consider a class of nonautonomous stochastic evolution equations in real separable Hilbert spaces.

We establish a new composition theorem for square-mean almost automorphic functions under non-Lipschitz conditions.

We apply this new composition theorem as well as intermediate space techniques, Krasnoselskii fixed point theorem, and Banach fixed point theorem to investigate the existence of square-mean almost automorphic mild solutions.

Some known results are generalized and improved.