全空间RN上Kirchhoff型方程单侧全局分歧和保号解
Unilateral Global Bifurcation and One-Sign Solutions for Kirchhoff Type Problem in RN
沈文国1
作者信息
- 1. 广东科技学院通识教育学院,广东东莞 523083
- 折叠
摘要
本文研究了下列Kirchhoff型方程:{-M(∫RN|▽u|2dx)△u=λa(x)f(u),x∈RN,u=0,as|x|→+∞.建立了方程的单侧全局分歧结果.应用上述分歧结果,对于属于不同区间的值,得到了方程保号解的存在性,不存在性及解的确切个数.
Abstract
In this paper,we study the following Kirchhoff type problem:{-M(∫Rx|▽u|2dx)△u=λa(x)f(u),x∈RN,u=0,as|x|→+∞.Unilateral global bifur-cation result is established for this problem.As applications of the bifurcation result,we determine the intervals of λ for the existence,non-existence,and exact multiplicity of one-sign solutions for this problem.
关键词
单侧全局分歧/保号解/Kirchhoff型方程Key words
unilateral global bifurcation/one-sign solutions/Kirchhoff type problem引用本文复制引用
基金项目
National Natural Science Foundation of China(11561038)
出版年
2024
NETL
NSTL
万方数据