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

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

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    Y. Kan-on, Existence of positive travelling waves for generic Lotka-Volterra competition model with diffusion, Dynam. Contin. Discrete Impuls. Systems, 6 (1999), 345-365.

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    H. Kokubu, Homoclinic and heteroclinic bifurcations of vector fields, Japan J. Appl. Math., 5 (1988), 455-501.

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