Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 407352, 11 pages
Fixed Points and Stability in Neutral Stochastic Differential Equations with Variable Delays
1Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
2College of Business and Management, Sichuan University, Chengdu, Sichuan 610064, China
Received 4 April 2008; Accepted 9 June 2008
Academic Editor: Tomas Domínguez Benavides
Copyright © 2008 Meng Wu 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.
We consider the mean square asymptotic stability of a generalized
linear neutral stochastic differential equation with variable delays by using the fixed point
theory. An asymptotic mean square stability theorem with a necessary and sufficient condition
is proved, which improves and generalizes some results due to Burton, Zhang and Luo. Two
examples are also given to illustrate our results.