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The existence of coexistence solutions of a predator-prey model. (Chinese. English summary) Zbl 1413.35261
Summary: The coexistence solutions of a predator-prey model with homogeneous Dirichlet boundary value conditions are studied. Firstly, by using the principle of extremum and the Young inequality, a priori estimate of positive equilibrium solution is given. Secondly, the sufficient and necessary conditions for the existence of positive solutions to equilibrium equation are discussed through the fixed-point index, topological degree theory and spectral analysis methods. Finally, taking the death rate as the bifurcation parameter, the existence of positive solution to this system is derived by making use of local bifurcation theory.
35K57 Reaction-diffusion equations
35B09 Positive solutions to PDEs
35B45 A priori estimates in context of PDEs
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