收稿日期: 2008-02-27
修回日期: 2008-07-17
网络出版日期: 2009-03-15
基金资助
supported by Natural Science Basic Research Plan in Shaanxi Province of China(2006A09)
Positive solutions for semilinear elliptic equations with critical Sobolev exponents
Received date: 2008-02-27
Revised date: 2008-07-17
Online published: 2009-03-15
Supported by
supported by Natural Science Basic Research Plan in Shaanxi Province of China(2006A09)
在 R n中具有光滑边界的有界域Ω内考虑具有Dirichlet边界条件的半线性椭圆方程- Δ u-μ u ｜x｜2 =g(x,u)+｜u｜2*-2u,这里g(x,·)在无穷远处具有次临界增长.由变分法,利用Brézis和Nirenberg "Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Comm. Pure Appl. Math. 1983, 36: 437~477" 的思想,证明了正解的存在性.
关键词： Sobolev临界指数; Hardy位势; 山路引理
郭千桥 , 崔学伟 . 具有Sobolev临界指数的半线性椭圆方程的正解[J]. 中国科学院大学学报, 2009 , 26(2) : 158 -166 . DOI: 10.7523/j.issn.2095-6134.2009.2.003
We consider the following semilinear elliptic equation - Δ u-μ u ｜x｜2 =g(x,u)+｜u｜2*-2u in Ω with Dirichlet boundary condition, where g(x,·) has subcritical growth at infinity. The existence of positive solutions are obtained by variational method in the spirit of Brézis-Nirenberg.
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