Abstract
In this paper, we consider a system of reaction-diffusion equations with competitive interaction, and discuss the structure of the set of stationary solutions for the system. To do this, our main tools are the comparison principle and the bifurcation theory.
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References
A. Coddington and N. Levinson, Theory of Ordinary Differential Equations. McGraw-Hill, New York-Toronto-London, 1955.
J.K. Hale, Asymptotic Behavior of Dissipative Systems. American Mathematical Society, Providence, RI, 1988.
Y. Kan-on, Bifurcation structure of stationary solutions of a Lotka-Volterra competition model with diffusion. SIAM J. Math. Anal.,29 (1998), 424–436.
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.
Y. Kan-on, On the structure of the set of stationary solutions for a Lotka-Volterra competition model with diffusion. Dynam. Contin. Discrete Impuls. Systems, Ser. B, Appl. Algorithms,8 (2001), 263–273.
K. Kishimoto and H.F. Weinberger, The spatial homogeneity of stable equilibria of some reaction-diffusion systems on convex domains. J. Differential Equations,58 (1985), 15–21.
P.H. Rabinowitz, Some global results for nonlinear eigenvalue problems. J. Funct. Anal.,7 (1971), 487–513.
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Kan-on, Y. On the structure of the set of stationary solutions for a system of reaction-diffusion equations with competitive interaction. Japan J. Indust. Appl. Math. 22, 385–402 (2005). https://doi.org/10.1007/BF03167491
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DOI: https://doi.org/10.1007/BF03167491