MONOTONE METHODS AND STABILITY RESULTS FOR NONLOCAL REACTION-DIFFUSION EQUATIONS WITH TIME DELAY | Zendy

Yueding Yuan | Zendy; Zhiming Guo | Zendy

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MONOTONE METHODS AND STABILITY RESULTS FOR NONLOCAL REACTION-DIFFUSION EQUATIONS WITH TIME DELAY

Author(s) -

Yueding Yuan,

Zhiming Guo

Publication year - 2018

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2018.1342

Subject(s) - monotone polygon , mathematics , a priori and a posteriori , stability (learning theory) , reaction–diffusion system , steady state (chemistry) , diffusion , mathematical analysis , computer science , physics , thermodynamics , chemistry , philosophy , geometry , epistemology , machine learning

In this paper, we study the applications of the monotone iteration method for investigating the existence and stability of solutions to nonlocal reaction-diffusion equations with time delay. We emphasize the importance of the idea of monotone iteration schemes for investigating the stability of solutions to such equations. We show that every steady state of such equations obtained by using the monotone iteration method is priori stable and all stable steady states can be obtained by using such method. Finally, we apply our main results to three population models.

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