STABILITY RESULTS OF RANDOM IMPULSIVE SEMILINEAR DIFFERENTIAL EQUATIONS

• Published in: Acta mathematica scientia Vol. 34; no. 4; pp. 1055 - 1071
• Main Authors: GOWRISANKAR, M., MOHANKUMAR, P., VINODKUMAR, A.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2014; 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
• Subjects: 35B35; 35R12; 35R60; 60H99; contraction principle; Differential equations; exponential stability; Hyers-Ulam stability; Hyers-Ulam-Rassias stability; Mapping; random impulses; semilinear differential equations; Stability; Uniqueness; 半线性微分方程; 压缩映射原理; 应用程序; 指数稳定性; 随机脉冲; 60H99; 35R60; Hyers-Ulam-Rassias stability; 35B35; 35R12; random impulses; semilinear differential equations; Hyers-Ulam stability; stability; exponential stability; contraction principle; stability,Hyers-Ulam sta-bility; contraction princi-ple
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(14)60069-2

In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilineax 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.