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

Abstract

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 m m in this model plays a very important role. A good understanding of the existence, stability and number of positive solutions is gained when m m is large. In particular, we obtain various results on the exact number of positive solutions. Our results for large m m reveal interesting contrast with that for the well-studied case m = 0 m=0 , i.e., the classical Lotka-Volterra predator-prey model.