具避难所的捕食-食饵模型非常数正解的存在性

考虑了一个齐次Neumann边界条件下具避难所的捕食-食铒模型的平衡态问题, 获得了该模型正平衡态解的进一步结果。给出了正解的先验估计,并用能量方法 得到其非常数正解的不存在性,利用拓扑度理论得出其非常数正解的存在性。

Existence of positive non-constant steady-states solutions to a prey-predator system incorporating a prey refuge

The steady-states of a diffusive prey-predator system incorporating a prey refuge subject to homogeneous Neumann boundary condition were considered,and some improved results of the positive steady states solutions were derived.A priori estimates for positive solutions were established,and the non-existence of non-constant positive steady states was given by using the energy method.The existence of non-constant positive steady states was obtained by using the topological degree theory.