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Coexistence Solutions for a Periodic Competition Model with Singular–Degenerate Diffusion

Part of: Partial differential equations Nonlinear operators and their properties Parabolic equations and systems

Published online by Cambridge University Press:  15 December 2016

Yifu Wang ,
Jingxue Yin  and
Yuanyuan Ke
Yifu Wang
Affiliation:
Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, People's Republic of China
Jingxue Yin
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, People's Republic of China
Yuanyuan Ke*
Affiliation:
School of Information, Renmin University of China, Beijing, 100872, People's Republic of China (keyy@ruc.edu.cn)
*
*Corresponding author.
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Abstract

We investigate a system of singular–degenerate parabolic equations with non-local terms, which can be regarded as a spatially heterogeneous competition model of Lotka–Volterra type. Applying the Leray–Schauder fixed-point theorem, we establish the existence of coexistence periodic solutions to the problem, which, together with the existing literature, gives a complete picture for such a system for all parameters.

Keywords

coexistence solutionsperiodic competition modelsingular–degenerate diffusion

MSC classification

Secondary: 35K65: Degenerate parabolic equations 35B10: Periodic solutions 47H10: Fixed-point theorems
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 4 , November 2017 , pp. 1065 - 1075
Copyright
Copyright © Edinburgh Mathematical Society 2017 

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