具有Sobolev临界指数的半线性椭圆方程的正解

doi:10.7523/j.issn.2095-6134.2009.2.003

中国科学院大学学报 ›› 2009, Vol. 26 ›› Issue (2): 158-166.DOI: 10.7523/j.issn.2095-6134.2009.2.003

具有Sobolev临界指数的半线性椭圆方程的正解

郭千桥, 崔学伟

西北工业大学应用数学系, 西安 710072

收稿日期:2008-02-27 修回日期:2008-07-17 发布日期:2009-03-15
通讯作者: 郭千桥
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

GUO Qian-Qiao, CUI Xue-Wei

Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, China

Received:2008-02-27 Revised:2008-07-17 Published:2009-03-15
Supported by:
supported by Natural Science Basic Research Plan in Shaanxi Province of China(2006A09) 

摘要/Abstract

摘要：

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^*-2}u,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

Abstract:

We consider the following semilinear elliptic equation - Δ u-μ u ｜x｜² =g(x,u)+｜u｜^{2^*-2}u 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.

Key words: critical Sobolev exponents, Hardy potentials, mountain pass lemma

中图分类号:

O175.25

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.

GUO Qian-Qiao, CUI Xue-Wei. Positive solutions for semilinear elliptic equations with critical Sobolev exponents[J]. , 2009, 26(2): 158-166.

参考文献

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具有Sobolev临界指数的半线性椭圆方程的正解

Positive solutions for semilinear elliptic equations with critical Sobolev exponents

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