The existence and exponential stability of semilinear functional differential equations with random impulses under non-uniqueness

被引：41

作者：

Anguraj, A. ^{[1
]}

Wu, Shujin ^{[2
]}

Vinodkumar, A. ^{[1
]}

机构：

[1] PSG Coll Arts & Sci, Dept Math, Coimbatore 641014, Tamil Nadu, India

[2] E China Normal Univ, Sch Finance & Stat, Dept Stat & Actuarial Sci, Shanghai 200241, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 02期

基金：

上海市自然科学基金; 中国国家自然科学基金;

关键词：

Mild solutions; Semilinear differential equation; Random impulse; Existence; Exponential stability; Leray-Schauder alternative fixed point theorem; FIXED-POINTS; SYSTEMS;

D O I：

10.1016/j.na.2010.07.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the existence and exponential stability of mild solutions of semilinear differential equations with random impulses are studied under non-uniqueness in a real separable Hilbert space. The results are obtained by using the Leray-Schauder alternative fixed point theorem. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：331 / 342

页数：12

共 14 条

[1] Existence results for an impulsive neutral functional differential equation with state-dependent delay
Anguraj, A.
Arjunan, M. Mallika
Hernandez, Eduardo M.
[J]. APPLICABLE ANALYSIS, 2007, 86 (07) : 861 - 872
[2] [Anonymous], DYNAM CONT DIS SER A
[3] [Anonymous], 1995, World Sci. Ser. Nonlinear Sci., Ser. A., DOI DOI 10.1142/2892
[4] Benchohra M, 2006, J APPL MATH STOCH AN, V2006, P1
[5] Fixed points and stability of an integral equation: Nonuniqueness
Burton, TA
Zhang, B
[J]. APPLIED MATHEMATICS LETTERS, 2004, 17 (07) : 839 - 846
[6] Da Prato G, 1992, STOCHASTIC EQUATIONS
[7] Existence of solutions for impulsive partial neutral functional differential equations
Hernandez M, Eduardo
Rabello, Marco
Henriquez, Hernan R.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 331 (02) : 1135 - 1158
[8] Lakshmikantham V., 1989, World scientific, V6
[9] 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
[10] Pazy A., 1983, SEMIGROUPS LINEAR OP, DOI [10.1007/978-1-4612-5561-1, DOI 10.1007/978-1-4612-5561-1]

← 1 2 →