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具Hardy-Sobolev临界指数的半线性椭圆方程的多解存在性 被引量：2

Multiple Nontrivial Solutions for Semilinear Elliptic Equations with Hardy-Sobolev Critical Exponent
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摘要 本文考虑一类具Hardy-Sobolve临界指数的半线性椭圆方程,通过证明局部(P．S．)条件和能量估计,运用伪指标理论得到了这类方程多解的存在性(见文[1-13])． We investigate a class of semilinear elliptic equations with Hardy-Sobolev critical exponent. With the aids of pseudoindex theory, multiple nontrivial solutions are obtained by proving local （P.S.） conditon and estimating energy carefully （see [1-13]）.
作者 杨敏波 沈自飞
机构地区 浙江师范大学数学系
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2006年第4期819-826,共8页 Acta Mathematica Sinica：Chinese Series
基金 国家自然科学基金资助项目(10471113)浙江省自然科学基金资助项目(M103098)
关键词 多解 HARDY-SOBOLEV临界指数 (P.S.)条件 multiple solutions Hardy-Sobolev critical exponent （P.S.） conditon
分类号 O175.25 [理学—基础数学]
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参考文献13

  • 1Brezis H.,Nirenberg L.,Positive solutions of nonlinear elliptic equations involving critical exponents,Comm.Pure Appl.Math.,1983,34:437-477.
  • 2Caffarelli L.,Kohn R.,Nirenberg L.,First order interpolation inequality with weights,Compositio Mathematica,1984,53:259-275.
  • 3Ghoussoub N.,Yuan C.,Multiple solutions for quasilinear PDEs involving the critical Sobolev and Hardy exponent,Trans.Amer.Math.Soc.,2000,352:5703-5743.
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同被引文献9

  • 1沈尧天,李周欣.含临界指数的p-Laplacian方程的特征值问题[J].华南理工大学学报（自然科学版）,2005,33(11):111-114. 被引量：3
  • 2吴波,沈自飞,杨敏波.具Hardy-Sobolev临界指数的奇异椭圆方程多解的存在性(英文)[J].应用泛函分析学报,2006,8(2):118-125. 被引量：2
  • 3[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[3]Padilla P.The Effect of the Shape of the Domain on the Existence of Solutions of an Equation Involving the Critical Sobolev Exponent[J].J Differential Equations,1996,124(2):449 -471.
  • 6[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.
  • 7[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.
  • 8[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.
  • 9[8]Chen J Q.Multiple Positive Solutions for a Class of Nonlinear Elliptic Equations[J].J Math Anal Appl,2004,295(2):341-354.

引证文献2

二级引证文献12

数学学报（中文版）
2006年 第4期

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