Positive steady state solutions of a diffusive Leslie-Gower predator-prey model with Holling type II functional response and cross-diffusion

Jun Zhou; Chan-Gyun Kim; Junping Shi

doi:10.3934/dcds.2014.34.3875

Article Contents

2014, Volume 34, Issue 9: 3875-3899. Doi: 10.3934/dcds.2014.34.3875

This issue Previous Article Dimension estimates in non-conformal setting Next Article

Positive steady state solutions of a diffusive Leslie-Gower predator-prey model with Holling type II functional response and cross-diffusion

1.
School of Mathematics and Statistics, Southwest University, Chongqing, 400715
2.
Department of Mathematics, College of William and Mary, Williamsburg, Virginia, 23187-8795

Received: August 2013

Revised: November 2013

Published: September 2014

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Abstract

In this paper we consider a diffusive Leslie-Gower predator-prey model with Holling type II functional response and cross-diffusion under zero Dirichlet boundary condition. By using topological degree theory, bifurcation theory, energy estimates and asymptotic behavior analysis, we prove the existence, uniqueness and multiplicity of positive steady states solutions under certain conditions on the parameters.

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Mathematics Subject Classification: 35J57, 35K55, 92C15, 92C40.

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