On the existence and uniqueness of positive solutions for competing species models with diffusion

Dancer, E. N.

doi:10.1090/S0002-9947-1991-1028757-9

On the existence and uniqueness of positive solutions for competing species models with diffusion
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Trans. Amer. Math. Soc. 326 (1991), 829-859 Request permission

Abstract:

In this paper, 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.

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