A Lotka-Volterra competition model with cross-diffusion. (English) Zbl 1276.92099

Summary: A Lotka-Volterra competition model with cross-diffusions under homogeneous Dirichlet boundary condition is considered, where cross-diffusions are included in such a way that the two species run away from each other because of the competition between them. Using the method of upper and lower solutions, sufficient conditions for the existence of positive solutions are provided when the cross-diffusions are sufficiently small. Furthermore, the investigation of nonexistence of positive solutions is also presented.


92D40 Ecology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
Full Text: DOI


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