Some uniqueness and exact multiplicity results for a predator-prey model

In this paper, we consider positive solutions of a predator-prey model with diffusion and under homogeneous Dirichlet boundary conditions. It turns out that a certain parameter in this model plays a very important role. A good understanding of the existence, stability and number of positive solutions is gained when is large. In particular, we obtain various results on the exact number of positive solutions. Our results for large reveal interesting contrast with that for the well-studied case , i.e., the classical Lotka-Volterra predator-prey model.