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On the existence and uniqueness of positive solutions for competing species models with diffusion. (English) Zbl 0769.35016
Summary: We consider strictly positive solutions of competing species systems with diffusion under Dirichlet boundary conditions. We obtain a good understanding of when strictly positive solutions exist, obtain new nonuniqueness results and a number of other results, showing how complicated these equations can be. In particular, we consider how the shape of the underlying domain affects the behaviour of the equations.

MSC:
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
92D25 Population dynamics (general)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
47J05 Equations involving nonlinear operators (general)
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
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