Positive steady state solutions of a Leslie–Gower predator–prey model with Holling type II functional response and density-dependent diffusion |
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| Institution: | 1. Univ. Nice Sophia Antipolis, CNRS, Labo. J.-A. Dieudonné, UMR 7351, Parc Valrose, F-06108 Nice, France;2. Inria, Sophia Antipolis Méditerranée Research Centre, Project COFFEE, France;3. Inria, Sophia Antipolis Méditerranée Research Centre, Project CASTOR, France;1. Department of Orthopedic Surgery, Sapporo Medical University School of Medicine, Sapporo, Japan;2. Asari Chuo Hospital, Otaru, Japan |
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| Abstract: | In this paper, we consider a Leslie–Gower predator–prey model with Holling type II functional response and density-dependent diffusion under zero Dirichlet boundary condition. Using degree theory, bifurcation theory, energy estimates and asymptotical behavior analysis, the existence and multiplicity of positive steady state solutions were shown under certain conditions on the parameters. |
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