数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (4): 1055-1071.doi: 10.1016/S0252-9602(14)60069-2

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STABILITY RESULTS OF RANDOM IMPULSIVE SEMILINEAR DIFFERENTIAL EQUATIONS

M. GOWRISANKAR|P. MOHANKUMAR|A. VINODKUMAR   

  1. Department of Mathematics, Annapoorana Engineering College, Salem-636308, Tamil Nadu, India; Department of Mathematics, Arupadai Veedu Institute of Technology, Chennai-636104, Tamil Nadu, India; Department of Mathematics, PSG College of Technology, Coimbatore-641004, Tamil Nadu, India
  • 收稿日期:2013-07-26 修回日期:2013-10-26 出版日期:2014-07-20 发布日期:2014-07-20

STABILITY RESULTS OF RANDOM IMPULSIVE SEMILINEAR DIFFERENTIAL EQUATIONS

M. GOWRISANKAR|P. MOHANKUMAR|A. VINODKUMAR   

  1. Department of Mathematics, Annapoorana Engineering College, Salem-636308, Tamil Nadu, India; Department of Mathematics, Arupadai Veedu Institute of Technology, Chennai-636104, Tamil Nadu, India; Department of Mathematics, PSG College of Technology, Coimbatore-641004, Tamil Nadu, India
  • Received:2013-07-26 Revised:2013-10-26 Online:2014-07-20 Published:2014-07-20

摘要:

In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilinear differential equations un-der 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.

关键词: semilinear differential equations, random impulses, stability, Hyers-Ulam sta-bility, Hyers-Ulam-Rassias stability, exponential stability, contraction princi-ple

Abstract:

In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilinear differential equations un-der 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.

Key words: semilinear differential equations, random impulses, stability, Hyers-Ulam sta-bility, Hyers-Ulam-Rassias stability, exponential stability, contraction princi-ple

中图分类号: 

  • 35R12