Positive solutions of Kirchhoff type elliptic equations involving a critical Sobolev exponent

被引:88
作者
Naimen, Daisuke [1 ]
机构
[1] Osaka City Univ, Grad Sch Sci, Dept Math, Sumiyoshi Ku, Osaka 5588585, Japan
来源
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2014年 / 21卷 / 06期
关键词
Kirchhoff; Elliptic; Critical; Variational method; CRITICAL GROWTH; STANDING WAVES; EXISTENCE; MULTIPLICITY; STABILITY;
D O I
10.1007/s00030-014-0271-4
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper we investigate the following Kirchhoff type elliptic boundary value problem involving a critical nonlinearity: here is a bounded domain with smooth boundary and a + b > 0. Under several conditions on and , we prove the existence and nonexistence of solutions of (K1). This is some extension of a part of Brezis-Nirenberg's result in 1983.
引用
收藏
页码:885 / 914
页数:30
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