Existence, uniqueness, and controllability results for neutral FSDES in Hilbert spaces

Abstract

We establish results concerning the global existence, uniqueness, and controllability of mild solutions for a neutral functional stochastic differential equations with variable delay in a real separable Hilbert space. The results are obtained by imposing a so-called Caratheodory condition on the nonlinearities, which is weaker than the classical Lipschitz condition. Examples illustrating the applicability of the general theory are also provided.