| 具有Sobolev临界指数的半线性椭圆方程的正解 |
| |
| 作者姓名： | 郭千桥 崔学伟 |
| |
| 作者单位： | 西北工业大学应用数学系, 西安 710072 |
| |
| 基金项目： | supported by Natural Science Basic Research Plan in Shaanxi Province of China(2006A09) |
| |
| 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*-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 |
| 收稿时间： | 2008-02-27 |
| 修稿时间： | 2008-07-17 |
Positive solutions for semilinear elliptic equations with critical Sobolev exponents |
| |
| Authors: | GUO Qian-Qiao CUI Xue-Wei |
| |
| Institution: | Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, China |
| |
| Abstract: | 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. |
| |
| Keywords: | critical Sobolev exponents Hardy potentials mountain pass lemma |
|
| 点击此处可从《》浏览原始摘要信息 |
| 点击此处可从《》下载免费的PDF全文 |
|
