The effect of predator competition on positive solutions for a predator–prey model with diffusion

A diffusive predator–prey model with predator competition is considered under Dirichlet boundary conditions. Some existence and non-existence results are firstly obtained. Then by investigating the bifurcation of positive solutions, the multiplicity of positive solutions is established for suitably large mm. Furthermore, by meticulously analyzing the asymptotic behaviors of positive solutions when kk goes to ∞∞, we find that there is at most a positive solution for any c∈Rc∈R when kk is sufficiently large. At last, some numerical simulations are presented to supplement the analytic results in one dimension.