非线性项含零点的二阶Dirichlet问题结点解集的全局结构

吉林大学学报(理学版) ›› 2022, Vol. 60 ›› Issue (3): 481-486.

非线性项含零点的二阶Dirichlet问题结点解集的全局结构

杨伟

西北师范大学数学与统计学院, 兰州 730070

收稿日期:2021-07-09 出版日期:2022-05-26 发布日期:2022-05-26
通讯作者: 杨伟 E-mail:wyang_nwnu@163.com

Global Structure of Nodal Solution Set of Second-Order Dirichlet Problems of Nonlinear Terms with Zero Points

YANG Wei

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received:2021-07-09 Online:2022-05-26 Published:2022-05-26

摘要/Abstract

摘要： 用Rabinowitz全局分歧定理, 研究二阶Dirichlet边值问题结点解集的全局结构, 其中r为正参数, a: ［0,1］→［0,∞)连续且允许其在［0,1］的
部分真子区间上恒为0, f: R→R在0和∞处是渐近线性的且有两个非0零点.

关键词: 分歧方法, 连通分支, 零点, 结点解

Abstract: By using the Rabinowitz global bifurcation theorem, the author studies the global structure of nodal solution set of second-order Dirichlet boundary problem, where r is a positive parameter, a: ［0,1］→［0,∞) is continuous and allowed to be constant at 0 in some proper subinterval of ［0,1］. f: R→R is continuous, asymptotically linear at 0 and ∞. There are two non-zero zero points of f.

Key words: bifurcation method, connected branch, zero point, nodal solution

中图分类号:

O175.8

杨伟. 非线性项含零点的二阶Dirichlet问题结点解集的全局结构[J]. 吉林大学学报(理学版), 2022, 60(3): 481-486.

YANG Wei. Global Structure of Nodal Solution Set of Second-Order Dirichlet Problems of Nonlinear Terms with Zero Points[J]. Journal of Jilin University Science Edition, 2022, 60(3): 481-486.