Existence of Square-Mean Almost Automorphic Solutions to Stochastic Functional Integrodifferential Equations in Hilbert Spaces

Abstract EN

The existence and uniqueness of square-mean almost automorphic mild solution to a stochastic functional integrodifferential equation is studied.

Under some appropriate assumptions, the existence and uniqueness of square-mean almost automorphic mild solution is obtained by Banach’s fixed point theorem.

Particularly, based on Schauder’s fixed point theorem, the existence of square-mean almost automorphic mild solution is obtained by using the condition which is weaker than Lipschitz conditions.

Finally, an example illustrating our main result is given.