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Coexistence theorem of steady states for nonlinear self-cross diffusion systems with competitive dynamics. (English) Zbl 1115.35321
Summary: In this paper, we discuss the existence of positive solutions to certain nonlinear elliptic systems representing competitive interaction with self-cross diffusions between two species. The method employed is the fixed point index theory in a positive cone. Sufficient conditions for the existence of positive solutions are provided.

MSC:
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
35K57 Reaction-diffusion equations
92D25 Population dynamics (general)
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