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p th Moment Stability of a Stationary Solution for a Reaction Diffusion System with Distributed Delays

Author

Listed:
  • Xiongrui Wang

    (College of Mathematics, Yibin University, Yibin 644000, China)

  • Ruofeng Rao

    (Department of Mathematics, Chengdu Normal University, Chengdu 611130, China)

  • Shouming Zhong

    (College of mathematics, University of Electronic Science and Technology of China, Chengdu 611731, China)

Abstract

In this paper, the Sobolev embedding theorem, Holder inequality, the Lebesgue contrl convergence theorem, the operator norm estimation technique, and critical point theory are employed to prove the existence of nontrivial stationary solution for p -Laplacian diffusion system with distributed delays. Furthermore, by giving the definition of p th moment stability, the authors use the Lyapunovfunctional method and Kamke function to derive the stability of nontrivialstationary solution. Moreover, a numerical example illuminates the effectiveness of the proposed methods. Finally, an interesting further thought is put forward, which is conducive to the in-depth study of the problem.

Suggested Citation

  • Xiongrui Wang & Ruofeng Rao & Shouming Zhong, 2020. "p th Moment Stability of a Stationary Solution for a Reaction Diffusion System with Distributed Delays," Mathematics, MDPI, vol. 8(2), pages 1-10, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:200-:d:317042
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    References listed on IDEAS

    as
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    5. Xiongrui Wang & Ruofeng Rao & Shouming Zhong, 2017. "New Stability Criterion for Takagi-Sugeno Fuzzy Cohen-Grossberg Neural Networks with Probabilistic Time-Varying Delays," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-11, November.
    6. Li, Xiaodi & Yang, Xueyan & Huang, Tingwen, 2019. "Persistence of delayed cooperative models: Impulsive control method," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 130-146.
    7. Li, Yongkun, 2005. "Global exponential stability of BAM neural networks with delays and impulses," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 279-285.
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