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具有Hardy项和Sobolev-Hardy临界指数的半线性椭圆方程解的存在性与多重性注记

A Remark on Existence and Multiplicity of Solutions for Semilinear Elliptic Equations with Hardy Terms and Sobolev-Hardy Critical Exponents
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摘要 用山路引理和一些分析技巧证明了一类具有Hardy项和Sobolev-Hardy临界指数的半线性椭圆方程的非线性项在弱的条件下解的存在性和多重性。 In this paper, using the Mountain Pass Lemma and some analysis techniques, the authors proved the existence and multiplicity of solutions for semilinear elliptic equations with Hardy terms and Sobolev-Hardy critical exponents under weak conditions.
作者 丁凌 孟义杰
机构地区 襄樊学院数学系
出处 《孝感学院学报》 2008年第3期19-22,共4页 JOURNAL OF XIAOGAN UNIVERSITY
关键词 Hardy项 SOBOLEV-HARDY临界指数 山路引理 存在性与多重性 (PS)条件 Hardy terms Sobolev- Hardy critical exponents the Mountain Pass Lemma existence and multiplicity （PS） condition
分类号 O176.3 [理学—基础数学]
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参考文献6

  • 1Ferrero A,Gazzola F. Existence of solutions for singular critical growth semi-linear elliptic equations[J]. J Differential Equations,2001,177 (2):494 -522.
  • 2Garcia Azorero J P, Peral Alonso I. Hardy inequalities and some critical elliptic and parabolic problems [J]. J Differential Equations,1998,144 (2):441- 476.
  • 3Ghoussoub N, Yuan C. Multiple solutions for quasilinear PDEs involving the critical Sobolev and Hardy exponents[J]. Trans Amer Math Soe,2000,352 (12) : 5703-5743.
  • 4Chen Jianqing. Multiple positive solutions for a class of nonlinear elliptic equations[J]. J Math Anal Appl, 2004,295 (2) :341-354.
  • 5Ding Ling, Tang Chunlei. Existence and multiplicky of semilinear elliptic equations involving Hardy term and Hardy-Sobolev critical exponents[J]. Appl Math Lett, 2007, 20 (12): 1175-1183.
  • 6丁凌,唐春雷.具有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）,2007,29(4):5-10. 被引量：12

二级参考文献8

  • 1杨敏波,沈自飞.具Hardy-Sobolev临界指数的半线性椭圆方程的多解存在性[J].数学学报（中文版）,2006,49(4):819-826. 被引量：2
  • 2[1]Brezis H,Nirenberg L.Positive Solutions of Nonlinear Elliptic Equations Involving Critical Sobolev Exponents[J].Comm Pure Appl Math,1983,36(4):437 -477.
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  • 5[5]Ferrero A,Gazzola F.Existence of Solutions for Singular Critical Growth Semi-Linear Elliptic Equations[J].J Differential Equations,2001,177(2):494-522.
  • 6[6]Ghoussoub N,Yuan C.Multiple Solutions for Quasi-Linear PDEs Involving the Critical Sobolev and Hardy Exponents[J].Trans Amer Math Soc,2000,352(12):5703-5743.
  • 7[7]Garcia Azorero J P,Peral Alonso I.Multiplicity of Solutions for Elliptic Problems with Critical Exponent or with a Nonsymmetric Term[J].Trans Amer Math Soc,1991,323(2):877-895.
  • 8[8]Chen J Q.Multiple Positive Solutions for a Class of Nonlinear Elliptic Equations[J].J Math Anal Appl,2004,295(2):341-354.

共引文献11

孝感学院学报
2008年 第3期

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