Global attracting set and stability of stochastic neutral partial functional differential equations with impulses

被引：44

作者：

Long, Shujun ^{[1
,2
]}

Teng, Lingying ^{[1
,3
]}

Xu, Daoyi ^{[1
]}

机构：

[1] Sichuan Univ, Yangtze Ctr Math, Chengdu 610064, Peoples R China

[2] Leshan Normal Univ, Coll Math & Informat Sci, Leshan 614004, Peoples R China

[3] SW Univ Nationalities, Coll Comp Sci & Technol, Chengdu 610041, Peoples R China

来源：

STATISTICS & PROBABILITY LETTERS | 2012年 / 82卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Global attracting set; Stochastic; Neutral; Impulse; Impulsive-integral inequality; EXPONENTIAL STABILITY; MILD SOLUTIONS; ASYMPTOTIC STABILITY; MEAN-SQUARE; INVARIANT;

D O I：

10.1016/j.spl.2012.05.018

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, a class of stochastic neutral partial functional differential equations with impulses is investigated. To this end, we first establish a new impulsive-integral inequality, which improve the inequality established by Chen [Chen, H.B., 2010. Impulsive-integral inequality and exponential stability for stochastic partial differential equation with delays. Statist. Probab. Lett. 80.50-56]. By using the new inequality, we obtain the global attracting set of stochastic neutral partial functional differential equations with impulses. Especially, the sufficient conditions ensuring the exponential p-stability of the mild solution of the considered equations are obtained. Our results can generalize and improve the existing works. An example is given to demonstrate the main results. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：1699 / 1709

页数：11

共 26 条

[11] Positive invariant and global exponential attractive sets of neural networks with time-varying delays
Liao, Xiaoxin
Luo, Qi
Zeng, Zhigang
[J]. NEUROCOMPUTING, 2008, 71 (4-6) : 513 - 518
[12] On the exponential stability in mean square of neutral stochastic functional differential equations
Liu, K
Xia, XW
[J]. SYSTEMS & CONTROL LETTERS, 1999, 37 (04) : 207 - 215
[13] Liu K., 1998, Stochastics, V63, P1
[14] Liu K., 2006, Stability of infinite dimensional stochastic differential equations with applications
[15] The Fundamental Solution and Its Role in the Optimal Control of Infinite Dimensional Neutral Systems
Liu, Kai
[J]. APPLIED MATHEMATICS AND OPTIMIZATION, 2009, 60 (01) : 1 - 38
[16] Stability of stochastic partial differential equations with infinite delays
Luo, Jiaowan
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 222 (02) : 364 - 371
[17] Fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays
Luo, Jiaowan
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 342 (02) : 753 - 760
[18] Exponential stability for stochastic neutral partial functional differential equations
Luo, Jiaowan
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 355 (01) : 414 - 425
[19] Pazy A., 2012, Semigroups of Linear Operators and Applications to Partial Differential Equations, DOI DOI 10.1007/978-1-4612-5561-1
[20] Asymptotic stability of second-order neutral stochastic differential equations
Sakthivel, R.
Ren, Yong
Kim, Hyunsoo
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2010, 51 (05)

← 1 2 3 →