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

[1] Anguraj A., 2010, Journal of Applied Mathematics and Informatics, V28, P739
[2] Existence, uniqueness and stability results of random impulsive semilinear differential systems
Anguraj, A.
Vinodkumar, A.
[J]. NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2010, 4 (03) : 475 - 483
[3] On the stability of invariant sets of functional differential equations
Bernfeld, SR
Corduneanu, C
Ignatyev, AO
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 55 (06) : 641 - 656
[4] Exponential stability of mild solutions of stochastic partial differential equations with delays
Caraballo, T
Liu, K
[J]. STOCHASTIC ANALYSIS AND APPLICATIONS, 1999, 17 (05) : 743 - 763
[5] Caraballo T., 1990, Stochastics and Stochastics Reports, V33, P27, DOI 10.1080/17442509008833662
[6] Caraballo T., 2007, DISCRETE CONTIN DYN, V18, P259
[7] Impulsive-integral inequality and exponential stability for stochastic partial differential equations with delays
Chen, Huabin
[J]. STATISTICS & PROBABILITY LETTERS, 2010, 80 (01) : 50 - 56
[8] Exponential stability for neutral stochastic partial differential equations with delays and Poisson jumps
Cui, Jing
Yan, Litan
Sun, Xichao
[J]. STATISTICS & PROBABILITY LETTERS, 2011, 81 (12) : 1970 - 1977
[9] Govindan T.E., 2005, Stochastics, V77, P139
[10] Exponential stability in mean-square of parabolic quasilinear stochastic delay evolution equations
Govindan, TE
[J]. STOCHASTIC ANALYSIS AND APPLICATIONS, 1999, 17 (03) : 443 - 461

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