Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 785628, 27 pages
doi:10.1155/2009/785628
Research Article

Existence and Stability of Solutions for Nonautonomous Stochastic Functional Evolution Equations

Xianlong Fu

Department of Mathematics, East China Normal University, Shanghai 200241, China

Received 19 March 2009; Accepted 2 June 2009

Academic Editor: Jozef Banas

Copyright © 2009 Xianlong Fu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We establish the results on existence and exponent stability of solutions for a semilinear nonautonomous neutral stochastic evolution equation with finite delay; the linear part of this equation is dependent on time and generates a linear evolution system. The obtained results are applied to some neutral stochastic partial differential equations. These kinds of equations arise in systems related to couple oscillators in a noisy environment or in viscoelastic materials under random or stochastic influences.