| 具有Sobolev临界指数的半线性椭圆方程的正解 |
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| 引用本文： | 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].中国科学院研究生院学报,2009,26(2):158-166. |
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| 作者姓名： | 郭千桥 崔学伟 |
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| 作者单位： | 西北工业大学应用数学系,西安,710072 |
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| 基金项目： | 陕西省国家重点基础研究发展规划(973计划) |
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| 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.
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| 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 |
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| GUO Qian-Qiao,CUI Xue-Wei.Positive solutions for semilinear elliptic equations with critical Sobolev exponents[J].Journal of the Graduate School of the Chinese Academy of Sciences,2009,26(2):158-166. |
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| Authors: | GUO Qian-Qiao CUI Xue-Wei |
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| Institution: | Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, China |
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| Abstract: | We consider the following semilinear elliptic equation -△u-μu/|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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| Keywords: | critical Sobolev exponents Hardy potentials mountain pass lemma |
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