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Qualitative analysis of a predator-prey system with Smith growth for prey. (Chinese. English summary) Zbl 1449.35266
Summary: A Holling type-III predator-prey model with Smith growth subject to the homogeneous Neumann boundary condition is investigated in this paper. Firstly, the local stability of positive constant steady state solution is discussed. Secondly, we give a priori estimate of positive solutions. Finally, some sufficient conditions for the nonexistence and existence of nonconstant positive steady state solutions are derived.
MSC:
35K57 Reaction-diffusion equations
35B09 Positive solutions to PDEs
35B35 Stability in context of PDEs
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