具有种内相食的捕食-食饵模型正解的惟一性  

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

作　　者：李兵方[1] 郭改慧[2] 白云霄[2] 

机构地区：[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

出　　处：《山东大学学报（理学版）》2013年第12期35-41,共7页Journal of Shandong University(Natural Science)

基　　金：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)

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。Under homogeneous Dirichlet boundary conditions, a predator-prey model with predator cannibalism is con- sidered. The existence and uniqueness of positive solutions are presented. By maximum principles and lower-upper solu-tion 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 u-niqueness of positive solutions is derived under some conditions.

关 键 词：种内相食 捕食-食饵 惟一性 

分 类 号：O175.26[理学—数学]