一个具扩散的捕食模型非常数正解的存在性

Existence of Positive Non-constant Steady-state Solutions to a Prey-predator System with Diffusion

考虑一个Neumann边界条件下具扩散和Holling型功能反应的捕食-被捕食模型的平衡态问题,获得了该模型正平衡态解的一些结果.首先,给出了正解的先验估计,进而,用能量方法得到其非常数正解的不存在性,用拓扑度理论得出其非常数正解的存在性结果.

Considering the steady-states of a diffusive prey-predator model with Holling type functional response function and subjected to homogeneous Neumann boundary condition, some results of positive non- constant steady-state solutions are derived. First, a priori estimates for positive solutions is established;then, the non-exlstence of non-constant positive steady states is given by using the energy method; the existence of non-constant positive steady states is obtained by using the topological degree theory.