Asymptotic behavior of attracting and quasi-invariant sets of impulsive stochastic partial integrodifferential equations with delays and Poisson jumps

The Journal of Nonlinear Sciences and its Applications

article

K. Ramkumar¹  K. Ravikumar¹  Dimplekumar Chalishajar²  A. Anguraj¹ 

[1] Department of Mathematics, PSG College of Arts, Science;Department of Mathematics, Computer science, Mallory Hall, Virginia Military Institute

关键词: Exponential stability;    almost surely exponential stability;    mild solution;    attracting set;    quasi-invariant set;    Poisson jumps;    resolvent operator;   

DOI  :  10.22436/jnsa.014.05.04

学科分类：社会科学、人文和艺术（综合）

来源: Shomal University

【 摘 要 】

This paper is concerned with a class of impulsive stochastic partial integrodifferential equations (ISPIEs) with delays and Poisson jumps. First, using the resolvent operator technique and contraction mapping principle, we can directly prove the existence and uniqueness of the mild solution for the system mentioned above. Then we develop a new impulsive integral inequality to obtain the global, both \(p^{\rm th}\) moment exponential stability and almost surely exponential stability of the mild solution is established with sufficient conditions. Also, a numerical example is provided to validate the theoretical result.

【 授权许可】

Unknown