Ground state and multiple solutions for a critical exponent problem

被引：16

作者：

Chen, Z. ^{[1
]}

Shioji, N. ^{[2
]}

Zou, W. ^{[1
]}

机构：

[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

[2] Yokohama Natl Univ, Dept Math, Fac Engn, Hodogaya Ku, Yokohama, Kanagawa 2408501, Japan

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2012年 / 19卷 / 03期

基金：

日本学术振兴会;

关键词：

NONLINEAR ELLIPTIC PROBLEMS; CRITICAL DIMENSIONS; EQUATIONS; EXISTENCE; BIFURCATION;

D O I：

10.1007/s00030-011-0127-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the following Brezis-Nirenberg type critical exponent equation which is related to the Yamabe problem: -Delta u = lambda u + vertical bar u vertical bar(2*-2)u, u is an element of H-0(1)(Omega), where Omega is a smooth bounded domain in R-N (N >= 3) and 2* is the critical Sobolev exponent. We show that, if N >= 5, this problem has at least inverted right perpendicularN+1/2inverted left perpendicular pairs of nontrivial solutions for each fixed lambda >= lambda(1), where lambda(1) is the first eigenvalue of -Delta with the Dirichlet boundary condition. For N >= 3, we give energy estimates from below for ground state solutions.

引用

页码：253 / 277

页数：25