Fixed Points and Stability in Neutral Stochastic Differential Equations with Variable Delays

被引：0
作者：
Meng Wu
Nan-jing Huang
Chang-Wen Zhao
机构：
[1] Sichuan University,Department of Mathematics
[2] Sichuan University,College of Business and Management
来源：
Fixed Point Theory and Applications | / 2008卷
关键词：
Banach Space; Asymptotic Stability; Stochastic Differential Equation; Inverse Function; Contraction Mapping;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
引用
收藏
相关论文
共 9 条
[1]  
Burton TA(2003)Stability by fixed point theory or Liapunov theory: a comparison Fixed Point Theory 4 15-32
[2]  
Burton TA(2002)Liapunov functionals, fixed points, and stability by Krasnoselskii's theorem Nonlinear Studies 9 181-190
[3]  
Burton TA(2004)Fixed points and stability of a nonconvolution equation Proceedings of the American Mathematical Society 132 3679-3687
[4]  
Burton TA(2001)Fixed points and problems in stability theory for ordinary and functional differential equations Dynamic Systems and Applications 10 89-116
[5]  
Furumochi T(2007)Fixed points and stability of neutral stochastic delay differential equations Journal of Mathematical Analysis and Applications 334 431-440
[6]  
Luo J(2005)Fixed points and stability in differential equations with variable delays Nonlinear Analysis 63 e233-e242
[7]  
Zhang B(1997)Matrix Riccati equations and stability of stochastic linear systems with nonincreasing delays Functional Differential Equations 4 279-293
[8]  
Kolmanovskii VB(undefined)undefined undefined undefined undefined-undefined
[9]  
Shaikhet LE(undefined)undefined undefined undefined undefined-undefined
1