On stochastic delay evolution equations with non-lipschitz nonlinearities in Hilbert spaces

Abstract

In this paper, we study existence and exponential stability problems of mild solutions associated with stochastic delay evolution equations in Hilbert spaces. These problems are resolved using the properties of a stochastic convolution integral and a comparison principle by exploiting Holder-type conditions on the drift and diffusion terms. The results obtained here generalize the corresponding main results from [1, 3, 4, 9, 13, 16].