Non-constant positive steady states of a predator-prey system with non-monotonic functional response and diffusion

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 Mathematics Subject Classification 35J55, 92D25.