STABILITY RESULTS OF RANDOM IMPULSIVE SEMILINEAR DIFFERENTIAL EQUATIONS

被引：31
作者：
Gowrisankar, M. [1 ]
Mohankumar, P. [2 ]
Vinodkumar, A. [3 ]
机构：
[1] Annapoorana Engn Coll, Dept Math, Salem 636308, Tamil Nadu, India
[2] Arupadai Veedu Inst Technol, Dept Math, Madras 636104, Tamil Nadu, India
[3] PSG Coll Technol, Dept Math, Coimbatore 641004, Tamil Nadu, India
来源：
ACTA MATHEMATICA SCIENTIA | 2014年 / 34卷 / 04期
关键词：
semilinear differential equations; random impulses; stability; Hyers-Ulam stability; Hyers-Ulam-Rassias stability; exponential stability; contraction principle; EXPONENTIAL STABILITY; FIXED-POINTS; EXISTENCE; INCLUSIONS;
D O I：
10.1016/S0252-9602(14)60069-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilinear differential equations under sufficient condition. The results are obtained by using the contraction mapping principle. Finally an example is given to illustrate the applications of the abstract results.
引用
收藏
页码：1055 / 1071
页数：17
相关论文
共 31 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] The existence and exponential stability of semilinear functional differential equations with random impulses under non-uniqueness
    Anguraj, A.
    Wu, Shujin
    Vinodkumar, A.
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (02) : 331 - 342
  • [3] 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
  • [4] Anguraj A., 2009, Int. J. Nonlinear Sci., V8, P412
  • [5] [Anonymous], DYNAM CONT DIS SER A
  • [6] [Anonymous], 2011, ELECTRON J QUAL THEO
  • [7] [Anonymous], 1995, World Sci. Ser. Nonlinear Sci., Ser. A., DOI DOI 10.1142/2892
  • [8] [Anonymous], 1968, COLLECTION MATH PROB
  • [9] [Anonymous], 2006, ACTA MATH APPL SIN-E
  • [10] Burton T. A., 2006, Stability by fixed point theory for functional differential equations
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