Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 934534, 11 pages
http://dx.doi.org/10.1155/2014/934534
Research Article

Asymptotically Almost Periodic Solutions for a Class of Stochastic Functional Differential Equations

1Educational Technology Center, Yulin Normal University, Yulin 537000, China
2School of Mathematics and Information Science, Yulin Normal University, Yulin 537000, China

Received 7 February 2014; Revised 29 March 2014; Accepted 29 March 2014; Published 6 May 2014

Academic Editor: Yonghui Xia

Copyright © 2014 Aimin Liu et al. 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

This work is concerned with the quadratic-mean asymptotically almost periodic mild solutions for a class of stochastic functional differential equations . A new criterion ensuring the existence and uniqueness of the quadratic-mean asymptotically almost periodic mild solutions for the system is presented. The condition of being uniformly exponentially stable of the strongly continuous semigroup is essentially removed, which is generated by the linear densely defined operator , only using the exponential trichotomy of the system, which reflects a deeper analysis of the behavior of solutions of the system. In this case the asymptotic behavior is described through the splitting of the main space into stable, unstable, and central subspaces at each point from the flow’s domain. An example is also given to illustrate our results.