摘要
文章研究一类具有Crowley-Martin反应函数的三种群在齐次Dirichlet边界条件下的捕食-食饵模型,首先借助于Frechet导数,利用线性算子的紧理论、不动点指数理论以及度的同伦不变性,得到了该系统在满足一定的条件下存在唯一的正解;其次运用椭圆型方程的正则理论,给出了该系统存在线性的、非退化的、稳定的正解的条件.
In this paper,a predator-prey model of three species with Crowley Martin response function under homogeneous dirichet boundary conditions is studied.Firstly,with the help of Frechet derivative,using the compact theory of linear operator,the fixed point index theory and the homotopy invariance of degree,it is obtained that the system has a unique positive solution under certain conditions;Secondly,using the regularization theory of elliptic equations,the conditions for the existence of linear,non degenerate and stable positive solutions of the system are given.
作者
董彪
蒲志林
DONG Biao;PU Zhi-lin(College of Mathematics,Aba Teachers University,Wenchuan 623002,China;College of Mathematics Science,Sichuan Normal University,Chengdu 610066,China)
出处
《数学的实践与认识》
北大核心
2025年第6期246-256,共11页
Mathematics in Practice and Theory
基金
四川省教育厅自然科学基金(15ZA0337)
四川省教育厅创新团队资助项目(18TD0047)
阿坝师范学院课题(201909003,201910132)。
