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

Volume 14, Issue 5, pp 339--350 http://dx.doi.org/10.22436/jnsa.014.05.04

Publication Date: February 28, 2021 Submission Date: December 08, 2020 Revision Date: December 30, 2020 Accteptance Date: January 15, 2021

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Authors

K. Ramkumar - Department of Mathematics, PSG College of Arts and Science, Coimbatore, 641 046, India. K. Ravikumar - Department of Mathematics, PSG College of Arts and Science, Coimbatore, 641 046, India. Dimplekumar Chalishajar - Department of Mathematics and Computer science, Mallory Hall, Virginia Military Institute, Lexington, VA 24450, USA. A. Anguraj - Department of Mathematics, PSG College of Arts and Science, Coimbatore, 641 046, India.

Abstract

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.

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Keywords

• Exponential stability
• almost surely exponential stability
• mild solution
• attracting set
• quasi-invariant set
• Poisson jumps
• resolvent operator

MSC

•  60H10
•  93E03
•  35B35
•  39B82

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