一类捕食-食饵模型正平衡解的存在性

Co-existence of positive steady-state solutions for a predator-prey model

本文利用锥映象不动点指数计算方法,结合极值原理、上下解方法及算子的谱分析,得出了一类Leslie-Gower和Holling-TypeII型捕食-食饵方程存在正平衡解的充分条件和必要条件,从结果中发现这两个条件之间有一段空隙.在此情形下,利用局部分歧理论讨论了正平衡解的存在性.

Coexistence positive solutions to the steady states of a predator-prey system with Leslie-Gower and Holling-Type Ⅱschemes is investigated in this paper. By means of calculating the indices of fixed points of compact maps in cones, in combination with the maximum principles, lower-upper solutions methods and spectrum analysis of operators, we obtain the necessary and sufficient conditions for existence of positive steady state solutions, but there is a gap between these two conditions, so we study the oositive solutions by using local bifurcation theorem in the case.