Non-autonomous stochastic evolution equations of parabolic type with nonlocal initial conditions

Abstract

In this paper, we study the non-autonomous stochastic evolution equations of parabolic type with nonlocal initial conditions in Hilbert spaces, where the operators in linear part (possibly unbounded) depend on time \begin{document}$ t $\end{document} and generate an evolution family. New existence result of mild solutions is established under more weaker conditions by introducing a new Green's function. The discussions are based on Schauder's fixed-point theorem as well as the theory of evolution family. At last, an example is also given to illustrate the feasibility of our theoretical results. The result obtained in this paper is a supplement to the existing literature and essentially extends some existing results in this area.