Structure on the set of radially symmetric positive stationary solutions for a competition-diffusion system

Yukio Kan-On

doi:10.3934/proc.2013.2013.427

Article Contents

2013, Volume 2013: 427-436. Doi: 10.3934/proc.2013.2013.427 open access

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Structure on the set of radially symmetric positive stationary solutions for a competition-diffusion system

Yukio Kan-On^1,

1.
Department of Mathematics, Faculty of Education, Ehime University, Matsuyama, 790-8577

Received: July 31, 2012

Revised: March 31, 2013

Published: October 2013

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Abstract

In this paper, we consider a reaction-diffusion system which describes the dynamics of population density for a two competing species community, and discuss the structure on the set of radially symmetric positive stationary solutions for the system by assuming the habitat of the community to be a ball. To do this, we shall treat the dimension of the habitat and the diffusion rates of the system as bifurcation parameters, and employ the comparison principle and the implicit function theorem.

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Mathematics Subject Classification: Primary: 35B32; Secondary: 35B60.

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References

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