• 论文 •

### 一类带有交叉扩散的捕食-食饵模型的正解

1. 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 Yuan1,2,*(),Yuping Wang1,Yanling Li3

1. 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)

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.

• O175.26