ON THE EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS FOR COMPETING SPECIES MODELS WITH DIFFUSION

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.