Kirchhoff-类椭圆方程的单边全局分歧和保号解的存在性问题
Unilateral Global Bifurcation and One-Sign Solutions for Kirchhoff-Type Elliptic Equations
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
将研究下列问题单边全局分歧及保号解的存在性{-M(∫Ω|▽u|2dx)△u=λa(x)f(u),x ∈ Ω,u=0,x ∈ ∂Ω,其中Ω是一个(R)N中有界并且在其边界上光滑的区域,M(·)∈C(R+),λ是一个参数,a(x)∈C((Ω),(0,+∞)),f∈C((R),(R)),对于 s≠0,满足 sf(s)＞0.当f0(∈)(0,+∞)或f∞(∈)(0,+∞)(其中 f0=lim|s|→0 f(s)/s,f∞=lim|s|→+∞ f(s)/s.),λ≠0 属于给定区间时,研究上述K-类方程保号解的存在性.我们用单边全局分歧技巧和连通序列集取极限的方法获得主要结果.
Abstract
In this paper,we study the unilateral global bifurcation and one-sign solutions for the following problems:{-M(∫Ω|▽u|2dx)△u=λa(x)f(u),in Ω,u=0,on ∂Ω,where Ω is a bounded domain in(R)N with a smooth boundary ∂Ω,M is a continuous function on(R)+,λ is a parameter,a(x)∈ C((Ω),(0,+oo)),f ∈ C((R),(R))with sf(s)＞0 for s ≠ 0.We give the intervals for the parameter λ≠0 which ensure the existence of positive solutions for the above Kirchhoff type equations if f0(∈)(0,∞)or f∞(∈)(0,∞),where f0=lim|s|→0f(s)/s,f∞=lim|s|→+∞ f(s)/s.We use Global bifurcation techniques and the approximation of connected components to prove our main results.
关键词
K-类方程/单边全局分歧/保号解/非线性项在零点和无穷远处非渐进增长Key words
Kirchhoff-type equations/unilateral global bifurcation/one-sign solutions/non-asymptotic nonlinearity at 0 or ∞引用本文复制引用
出版年
2024
NETL
NSTL
万方数据