APPROXIMATE CONTROLLABILITY OF NONLOCAL PROBLEM FOR NON-AUTONOMOUS STOCHASTIC EVOLUTION EQUATIONS

In this paper, we are considered with approximate controllability for a class of non-autonomous stochastic evolution equations of parabolic type with discrete nonlocal initial conditions. Some new results about existence of mild solutions as well as approximate controllability are established under more natural conditions on nonlinear functions and control operator by introducing a new Green function and using the theory of evolution family, Schauder fixed point theorem and the resolvent operator condition. At last, as a sample of application, these results are applied to a class of non-autonomous stochastic partial differential equation of parabolic type with discrete nonlocal initial conditions. The results obtained in this paper is a supplement to the existing literature and essentially extends some existing results in this area.