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

Abstract 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 m . Furthermore, by meticulously analyzing the asymptotic behaviors of positive solutions when k goes to ∞ , we find that there is at most a positive solution for any c ∈ R when k is sufficiently large. At last, some numerical simulations are presented to supplement the analytic results in one dimension.

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