Peter Y. H. Pang and Mingxin Wang

This paper deals with non-constant positive steady-state solutions of a predator-prey system with non-monotonic functional response, also called Holling type-IV interaction terms, and diffusion under the homogeneous Neumann boundary condition. We first establish positive upper and lower bounds for such solutions, and then study their non-existence, global existence and bifurcation.

2000 Mathematical Subject Classification: 35J55, 92D25.

Keywords: predator-prey model, non-constant positive steady states, bifurcation, global existence.

E-mail:
matpyh@nus.edu.sg
mxwang@seu.edu.cn