Fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays

被引：112

作者：

Luo, Jiaowan ^{[1
]}

机构：

[1] Guangzhou Univ, Sch Math & Informat Sci, Dept Probabil & Stat, Guangzhou 510405, Guangdong, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2008年 / 342卷 / 02期

基金：

中国国家自然科学基金;

关键词：

mild solution; stochastic delay partial differential equation; exponential stability;

D O I：

10.1016/j.jmaa.2007.11.019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The fixed-point theory is first used to consider the stability for stochastic partial differential equations with delays. Some conditions for the exponential stability in pth mean as well as in sample path of mild solutions are given. These conditions do not require the monotone decreasing behavior of the delays, which is necessary in [T. Caraballo, K. Liu, Exponential stability of mild solutions of stochastic partial differential equations with delays, Stoch. Anal. Appl. 17 (1999) 743-763; Ruhollan Jahanipur, Stability of stochastic delay evolution equations with monotone nonlinearity, Stoch. Anal. Appl. 21 (2003) 161-181]. Even in this special case, our results also improve the results in [T. Caraballo, K. Liu, Exponential stability of mild solutions of stochastic partial differential equations with delays, Stoch. Anal. Appl. 17 (1999) 743-763]. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：753 / 760

页数：8

共 50 条

[1] Exponential stability of mild solutions of stochastic partial differential equations with delays
Caraballo, T
Liu, K
STOCHASTIC ANALYSIS AND APPLICATIONS, 1999, 17 (05) : 743 - 763
[2] Fixed Points and Stability of Stochastic Neutral Partial Differential Equations with Infinite Delays
Luo, Jiaowan
Taniguchi, Takeshi
STOCHASTIC ANALYSIS AND APPLICATIONS, 2009, 27 (06) : 1163 - 1173
[3] Exponential stability of impulsive stochastic partial differential equations with delays
Li, Dingshi
Fan, Xiaoming
STATISTICS & PROBABILITY LETTERS, 2017, 126 : 185 - 192
[4] Exponential stability of energy solutions to stochastic partial differential equations with variable delays and jumps
Hou, Zhenting
Bao, Jianhai
Yuan, Chenggui
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 366 (01) : 44 - 54
[5] Exponential stability of mild solutions to impulsive stochastic neutral partial differential equations with memory
Yang, Hua
Jiang, Feng
ADVANCES IN DIFFERENCE EQUATIONS, 2013, : 1 - 9
[6] Exponential stability of mild solutions to impulsive stochastic neutral partial differential equations with memory
Hua Yang
Feng Jiang
Advances in Difference Equations, 2013
[7] Fixed Points and Stability in Neutral Stochastic Differential Equations with Variable Delays
Meng Wu
Nan-jing Huang
Chang-Wen Zhao
Fixed Point Theory and Applications, 2008
[8] Fixed points and stability in neutral stochastic differential equations with variable delays
Wu, Meng
Huang, Nan-Jing
Zhao, Chang-Wen
FIXED POINT THEORY AND APPLICATIONS, 2008, 2008 (1)
[9] FIXED POINTS AND EXPONENTIAL STABILITY OF ALMOST PERIODIC MILD SOLUTIONS TO STOCHASTIC VOLTERRA-LEVIN EQUATIONS
Tong Ouyang
Weiguo Liu
Annals of Applied Mathematics, 2015, 31 (02) : 190 - 199
[10] Fixed points and exponential stability of stochastic functional partial differential equations driven by fractional Brownian motion
Ruan, Dehao
Luo, Jiaowan
PUBLICATIONES MATHEMATICAE-DEBRECEN, 2015, 86 (3-4): : 285 - 293

← 1 2 3 4 5 →