具有种内相食的捕食-食饵模型正解的惟一性

J4 ›› 2013, Vol. 48 ›› Issue (12): 35-41.

具有种内相食的捕食-食饵模型正解的惟一性

李兵方1,郭改慧2,白云霄2

1.陕西铁路工程职业技术学院基础课部, 陕西渭南 714000; 2.陕西科技大学理学院, 陕西西安 710021

收稿日期:2013-04-10 出版日期:2013-12-20 发布日期:2014-01-09
作者简介:李兵方(1980- )，男，讲师，硕士，主要从事微分方程与高等数学研究. Email: bingfang@163.com
基金资助:
国家自然科学基金资助项目(11271236)；陕西省自然科学基础研究计划资助项目(2011JQ1015)；陕西省教育厅专项资助项目(12JK0856)；陕西科技大学自然科学基金资助项目(2012SB001)

The uniqueness of positive solutions for a predator-prey
model with predator cannibalism

LI Bing-fang1, GUO Gai-hui2, BAI Yun-xiao2

1. Department of Basic Course, Shaanxi Railway Institute, Weinan 714000, Shaanxi, China;
2. College of Science, Shaanxi University of Science and Technology, Xi’an 710021, Shaanxi, China

Received:2013-04-10 Online:2013-12-20 Published:2014-01-09

摘要/Abstract

摘要：

在齐次Dirichlet边界条件下研究一类种内相食的捕食-食饵模型正解的存在性和惟一性。首先利用极值原理、上下解方法给出正解的先验估计,然后利用LeraySchauder度理论, 通过计算锥映射不动点指标得到正解的存在性,最后利用特征值变分原理给出正解存在的惟一性。

关键词: 种内相食; 捕食-食饵; 惟一性

Abstract:

Under homogeneous Dirichlet boundary conditions, a predator-prey model with predator cannibalism is considered. The existence and uniqueness of positive solutions are presented. By maximum principles and lower-upper solution methods, a prior estimate of positive solutions is firstly obtained. Then by Leray-Schauder theory and resorting to calculate fixed point indices of compact maps in cones, sufficient conditions for coexistence are given. Moreover, the uniqueness of positive solutions is derived under some conditions.

Key words: predator cannibalism; predatorprey; uniqueness

中图分类号:

O175.26

李兵方1,郭改慧2,白云霄2. 具有种内相食的捕食-食饵模型正解的惟一性[J]. J4, 2013, 48(12): 35-41.

LI Bing-fang1, GUO Gai-hui2, BAI Yun-xiao2. The uniqueness of positive solutions for a predator-prey
model with predator cannibalism[J]. J4, 2013, 48(12): 35-41.

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