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带有临界指数的椭圆型方程的正解的存在性 被引量：4

Elliptic Problem with Critical Weighted Sobolev-Hardy Exponent
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摘要 本文主要采用变分方法来研究一类带有临界指数的椭圆型方程的正解的存在性问题.并且,在Ω领域(有界或无界)中的许多条件下,可以证明其基态解的存在性. This paper is devoted to the existence of positive solutions of a singular elliptic equation. Under various assumption on the domainΩ, which includes some kinds of unbounded domains,we have proved the existence of ground states.
作者 许勇强
机构地区 仰恩大学数学系
出处 《应用数学学报》 CSCD 北大核心 2007年第6期1130-1139,共10页 Acta Mathematicae Applicatae Sinica
关键词 临界指数 C—K—N不等式 集中紧性 critical Sobolev-Hardy exponent Caffarelli-Kohn-Nirenberg inequalities concentration-compactness
分类号 O175.25 [理学—基础数学]
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参考文献9

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  • 2Caffarelli L, Kohn R, Nirenberg. First order Interpolation Inequality with Weights. Compositio Math., 1984, 53:259-275.
  • 3Catrina F, Wang Z-Q. On the Caffarelli-Kohn-Nirenberg Inequalities: Sharp Constants Existence (and Nonexistence), and Symmetry of External Functions. Comm. Pure Appl. Math., 2001, 54:229-257.
  • 4Jannclli E. The Role Played by Space Dimension in Elliptic Critical Problems. J. Differential Equations, 1999, 156:407-426.
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同被引文献12

  • 1ALVES C O, FILHO D C , SOUTO M A S. On Systems of Elliptic Equations Involving Subcritical or Critical Sobolev Exponents [J]. Nonlinear Analysis, 2000, 42: 771-787.
  • 2CAFFARELLI L, KOHN R, NIRENBERG L. First Order Interpolation Inequality with Weights [J]. Compos Math, 1984, 53: 259-275.
  • 3CATRINA F, WANG Zhi-qiang. On the Caffareili-Kohn-Nirenberg Inequalities: Sharp Constants, Existence (and Non- existence), and Symmetry of Extermal Functions [J]. Comm Pure Appl Math, 2001, 54: 229-257.
  • 4KANG Dong-sheng. On Elliptic Problems with Critical Weighted Sobolev-Hardy Exponents [J]. Nonlinear Anal, 2007, 66 : 1037- 1050.
  • 5HUANG Li, WU Xing-ping, TANG Chun lei. Existence and Multiplicity of Solutions for Semilinear Elliptic Equations with Critical Weighted Hardy-Sobolev Exponents [J]. Nonlinear Anal, 2009, 71: 1916-1924.
  • 6LI Gong-bao, PENG Shuang-jie. Remarks on Elliptic Problems Involving the Caffarelli-Kohn-Nirenberg Inequalities [J]. Proc Amer Math Soe, 2008, 136: 1221-1228.
  • 7BARTSCH T, PENG Shuang-jie, ZHANG Zhi-tao. Existence or Nonexistence of Solutions to the Elliptic Equations Re lated to Caffarelli-Kohn-Nirenberg Inequalities [J]. Calc Var Part Differ Equat, 2007, 30: 113-136.
  • 8林美琳.一类带权的非线性椭圆方程正解的存在性问题[J].数学学报（中文版）,2009,52(1):171-180. 被引量：6
  • 9黄丽,,吴行平,唐春雷.具有加权Hardy-Sobolev临界指数的p-Laplacian方程解的存在性和多重性(英文)[J].西南大学学报（自然科学版）,2009,31(2):1-8. 被引量：2
  • 10吕登峰.一类含临界指数双调和椭圆方程组非平凡解的存在性[J].华中师范大学学报（自然科学版）,2010,44(3):382-385. 被引量：2

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应用数学学报
2007年 第6期

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