一类带有交叉扩散的捕食-食饵模型的正解

数学物理学报 ›› 2019, Vol. 39 ›› Issue (3): 545-559.

一类带有交叉扩散的捕食-食饵模型的正解

袁海龙^1,^2,*(),王玉萍¹,李艳玲³

¹ 陕西科技大学文理学院西安 710021
² 西安交通大学数学与统计学院西安 710049
³ 陕西师范大学数学与信息科学学院西安 710119

收稿日期:2018-04-20 出版日期:2019-06-26 发布日期:2019-06-27
通讯作者: 袁海龙 E-mail:yuanhailong@sust.edu.cn
基金资助:
国家自然科学基金(11271236);国家自然科学基金(61672021);国家自然科学基金(61872227);陕西科技大学博士科研启动基金(2017BJ-44)

Positive Solutions of a Predator-Prey Model with Cross Diffusion

Hailong Yuan^1,^2,*(),Yuping Wang¹,Yanling Li³

¹ School of Arts and Sciences, Shaanxi University of Science and Technology, Xi'an 710021
² School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049
³ School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119

Received:2018-04-20 Online:2019-06-26 Published:2019-06-27
Contact: Hailong Yuan E-mail:yuanhailong@sust.edu.cn
Supported by:
the NSFC(11271236);the NSFC(61672021);the NSFC(61872227);the Natural Science Foundation of Shaanxi University of Science and Technology(2017BJ-44)

摘要/Abstract

摘要：

该文研究了一类在齐次Dirichlet边界条件下的带有交叉扩散的捕食-食饵模型.首先，根据Leray-Schauder度理论，建立了系统的正解的存在性；其次，当参数m=β且充分大时，分别研究了正则扰动方程和奇异扰动方程的正解的存在性，和借助分歧理论说明奇异系统的正解在a^*处爆破；最后，建立了系统正解的多解性.

关键词: 交叉扩散, 分歧, 正解

Abstract:

A predator-prey model with cross diffusion under homogeneous Dirichlet boundary conditions is investigated. Firstly, the existence of positive solutions can be established by the Leray-Schauder degree theory. Secondly, we consider that the existence of positive solutions of the regular perturbation system and the singular perturbation system when m=β is sufficiently large, respectively, and moreover, we show that the positive solutions of the singular perturbation system will blow up along the continuum at a^* by the bifurcation theory. Finally, the multiplicity results of positive solutions of system is also considered.

Key words: Cross diffusion, Bifurcation, Positive solutions

中图分类号:

O175.26

袁海龙,王玉萍,李艳玲. 一类带有交叉扩散的捕食-食饵模型的正解[J]. 数学物理学报, 2019, 39(3): 545-559.

Hailong Yuan,Yuping Wang,Yanling Li. Positive Solutions of a Predator-Prey Model with Cross Diffusion[J]. Acta mathematica scientia,Series A, 2019, 39(3): 545-559.

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