Existence of positive solutions to a predator-prey model with diffusion

被引：0
|
作者：
Zhang Y. [1 ]
Chen W. [1 ]
机构：
[1] Department of Mathematics, Southeast University
来源：
Dongnan Daxue Xuebao (Ziran Kexue Ban)/Journal of Southeast University (Natural Science Edition) | 2010年 / 40卷 / 03期
关键词：
Existence; Fixed point index; Holling type-IV function; Predator-prey model;
D O I：
10.3969/j.issn.1001-0505.2010.03.042
中图分类号：
学科分类号：
摘要：
A predator-prey model with diffusion and a non-monotonic functional response, the Holling type-IV function, is discussed under homogeneous Dirichlet boundary conditions. First, the problem is equivalent to a strongly coupled elliptic boundary value problem and a priori estimate of positive solutions is deduced by means of the maximum principle and the upper and lower solution method. Then by changing the elliptic equations into a completely continuous operator and by combining with the topological degree theory in cones, sufficient conditions for the existence of positive solutions are given. Results show that the predator and prey can coexist when the prey has the ability of group defense or when anorexia response occurs on the predator population.
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收藏
页码：660 / 662
页数：2
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