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Positive steady states of a prey-predator model with diffusion and non-monotone conversion rate. (English) Zbl 1151.35341

Summary: We study the positive steady states of a prey-predator model with diffusion throughout and a non-monotone conversion rate under the homogeneous Dirichlet boundary condition. We obtain some results of the existence and non-existence of positive steady states. The stability and uniqueness of positive steady states are also discussed.

MSC:

35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35B25 Singular perturbations in context of PDEs
92C40 Biochemistry, molecular biology
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