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

J4 ›› 2011, Vol. 46 ›› Issue (2): 15-21.

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

姜良站,李艳玲*

陕西师范大学数学与信息科学学院, 陕西西安 710062

收稿日期:2009-10-26 出版日期:2011-02-16 发布日期:2011-03-30
通讯作者: 李艳玲(1963- ),女,教授,博士,硕士生导师,研究方向为反应扩散方程及其应用.
作者简介:姜良站(1983- ),男,硕士研究生,研究方向为反应扩散方程及其应用. Email:jiangliangzhan2001@yahoo.com.cn
基金资助:
国家自然科学基金资助项目（10571115）;陕西省自然科学基础研究资助项目（2007A11）

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

JIANG Liang-zhan, LI Yan-ling*

College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China

Received:2009-10-26 Online:2011-02-16 Published:2011-03-30

摘要/Abstract

摘要：

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。

关键词: 避难所;先验估计;非常数正解的存在性

Abstract:

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 priori-estimate 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.

Key words: prey refuge; priori estimate; non-constant positive solution existence

姜良站,李艳玲*. 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[J]. J4, 2011, 46(2): 15-21.

JIANG Liang-zhan, LI Yan-ling*. Existence of positive non-constant steady-states to a predator-prey system incorporating a constant prey refuge[J]. J4, 2011, 46(2): 15-21.

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