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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 486191, 11 pages
http://dx.doi.org/10.1155/2014/486191
Research Article

LaSalle-Type Theorems for General Nonlinear Stochastic Functional Differential Equations by Multiple Lyapunov Functions

Systems Engineering Institute, South China University of Technology, Guangzhou 510640, China

Received 18 August 2013; Revised 20 February 2014; Accepted 6 March 2014; Published 13 April 2014

Academic Editor: Narcisa C. Apreutesei

Copyright © 2014 Xueyan Zhao 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

We investigate LaSalle-type theorems for general nonlinear stochastic functional differential equations. With some preliminaries on lemmas and the derivation techniques, we establish three LaSalle-type theorems for the general nonlinear stochastic functional differential equations via multiple Lyapunov functions. For the typical special case with estimations involving for the derivatives of the Lyapunov functions, a theorem is established as the corollary of the main theorem. At the end of the paper, an example is given to illustrate the usage of the method proposed and show the advantage of the results obtained.