一类具有常数避难所的捕食-食饵模型非常数正解的存在性

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

研究一类具有常数避难所的两物种间的捕食-食饵模型。利用特征值理论得到正常数平衡解的稳定性结论;并且利用极值原理和Harnack不等式给出了系统正解的先验估计;最后,利用能量方法和拓扑度理论分别得出非常数正解的不存在性和非常数正解的存在性。

A kind of predator-prey model between two species incorporating a constant prey refuge is investigated. The stability of the positive constant solution of steady state system is discussed making use of eigenvalue theory. A prioriestimate of the positive solutions is given based on the maximum principle and Harnack inequality. Finally, by means of the energy method and topological degree theory, the non-existence of non-constant positive steady states is given and the existence of non-constant positive steady states is obtained, respectively.