Electron. J. Diff. Equ., Vol. 2016 (2016), No. 205, pp. 1-15.

Coexistence of steady state for a diffusive prey-predator model with harvesting

Yan Li

In this article, we study a diffusive prey-predator model with modified Leslie-Gower term and Michaelis-Menten type prey harvesting, subject to homogeneous Dirichlet boundary conditions. Treating the prey harvesting parameter as a bifurcation parameter, we obtain the existence, bifurcation and stability of coexistence steady state solutions. We use the method of upper and lower solutions, degree theory in cones, and bifurcation theory. The conclusions show the importance of prey harvesting in the model.

Submitted March 10, 2016. Published July 28, 2016.
Math Subject Classifications: 35J25, 35B09, 92B05.
Key Words: Michaelis-Menten type prey harvesting; coexistence solutions; upper and lower solutions method; degree theory; bifurcation theory.

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Yan Li
Department of Mathematics
China University of Petroleum
Qingdao 266580, China
email: liyan@upc.edu.cn

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