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Open AccessArticle

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

1
College of Mathematics, Yibin University, Yibin 644000, China
2
Department of Mathematics, Chengdu Normal University, Chengdu 611130, China
3
College of mathematics, University of Electronic Science and Technology of China, Chengdu 611731, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 200; https://doi.org/10.3390/math8020200
Received: 1 December 2019 / Revised: 24 January 2020 / Accepted: 30 January 2020 / Published: 6 February 2020
(This article belongs to the Special Issue Impulsive Control Systems and Complexity)
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 pth 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. View Full-Text
Keywords: large-scale variational methods; Lyapunovfunctional; pth moment stability large-scale variational methods; Lyapunovfunctional; pth moment stability
MDPI and ACS Style

Wang, X.; Rao, R.; Zhong, S. pth Moment Stability of a Stationary Solution for a Reaction Diffusion System with Distributed Delays. Mathematics 2020, 8, 200.

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