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一类半线性椭圆方程解的存在性 被引量：2

THE EXISTENCE OF SOLUTION FOR SEMILINEAR ELLIPTIC EQUATIONS
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摘要 本文研究了一类具有临界增长的半线性椭圆型方程.采用最近A.Ambrosetti所提出的扰动方法研究这类问题,得到这类问题的解的存在性.与通常所用的临界点理论方法相比较,本文解的存在性在较弱条件下可得. This paper studies a kind of semilinear elliptic equations. We obtain the solution of these equations via Perturbation method proposed by A. Ambrosetti recently. Compared with the classical critical theory,the existence of solution holds under a weaker condition.
作者 程铭东 徐彬
机构地区 黄石理工学院数理学院 华中师范大学数学与统计学院
出处 《数学杂志》 CSCD 北大核心 2008年第4期443-448,共6页 Journal of Mathematics
基金 国家自然科学基金资助项目(10471052)
关键词 半线性椭圆方程 扰动方法 存在性 semilinear elliptic equation perturbation method existence
分类号 O175.29 [理学—基础数学]
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参考文献9

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同被引文献17

  • 1Kang D S,Peng S J.Solutions for semi-linear elliptic problems with critical Sobolev-Hardy exponents and Hardy potential[J].Appl.Math.Lett.,2005,18(10):1094-1100.
  • 2Shen Z F,Yang M B.Nontrivial solution for Hardy-Sobolev critical elliptice equations[J].Acta.Math.Sinica,2005,48(5):999-1010.
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  • 4Chou K S,Chu C W.On the best constant for a weighted Sobolev-Hardy inequality[J].J.London Math.Soc.,1993,48(2):137-151.
  • 5Ghoussoub N,Kang X S.Hardy-Sobolev critical elliptic equations with boundary singularities[J].Ann.I.H.Poincare-AN,2004,21(6):767-793.
  • 6Ghoussoub 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.
  • 7Kang D S,Peng S J.Positive solutions for singular critical elliptic problems[J].Applied Math.Letters,2004,17(4):411-416.
  • 8Castro A,Maya C,Shivaji R.Nonlinear eigenvalue problems with semipositone structure[J].E.J.Diff.Eqns.,2000,5:33-49.
  • 9Castro A,Shivaji R.Nonnegative solutions for a class of nonpositone problems[J].Proc.Roy.Soc.Edin.,1988,108(A):291-302.
  • 10Anuradha A,Dickens S,Shivaji R.Existence results for nonautonomous elliptic boundary value problems[J].E.J.Diff.Eqns.,1994,1994(4):1-10.

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数学杂志
2008年 第4期

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