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带有多重临界指数的椭圆方程组的非平凡解 被引量：1

Nontrivial Solutions to Elliptic Systems Involving Multiple Critical Exponents
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摘要 研究了一类带有多重临界Sobolev指数和Hardy项的椭圆方程组,运用变分方法和分析技巧,证明了方程组对于大范围参变量非平凡解的存在性. In this paper,a system of elliptic equations is investigated,which involves multiple critical Sobolev exponents and Hardy-type terms.By variational methods and analytic techniques,the existence of nontrivial solutions to the system is established for large ranges of parameters.
作者 康东升 吴红 张微微
机构地区 中南民族大学数学与统计学学院
出处 《中南民族大学学报（自然科学版）》 CAS 2013年第1期92-96,共5页 Journal of South-Central University for Nationalities：Natural Science Edition
基金 国家民委科研基金资助项目(12ZNZ004)
关键词 椭圆方程组 解 临界指数 HARDY不等式 变分方法 elliptic system solution critical exponent Hardy inequality variational method
分类号 O175.25 [理学—基础数学]
  • 相关文献

参考文献8

  • 1Hardy G,Littlewood J,Polya G.Inequalities[M].Cambridge:Cambridge University Press,1988:239-243.
  • 2Egnell H.Elliptic boundary value problems with singularcoefficients and critical nonlinearities[J].Indiana UnivMath,1989,38(1):235-251.
  • 3Talenti G.Best constant in Sobolev inequality[J].AnnMat Pura Appl,1976,110(1):353-372.
  • 4Terracini S.On positive solutions to a class of equationswith a singular coefficient and critical exponent[J].AdvDifferential Equations,1996,2(1):241-264.
  • 5Huang Y,Kang D.On the singular elliptic systemsinvolving multiple critical Sobolev exponents[J].Nonlinear Anal,2011,74(2):400-412.
  • 6Cao D,Han P.Solutions for semilinear elliptic equationswith critical exponents and Hardy potential[J].JDifferential Equations,2004,205(2):521-537.
  • 7Ferrero A,Gazzola F.Existence of solutions for singularcritical growth semilinear elliptic Equations[J].JDifferential Equations,2001,177(1):494-522.
  • 8Rabinowitz P.Minimax methods in critical points theorywith applications to differential Equations[M].Washington:American Mathematical Society,1986:7-50.

同被引文献8

  • 1Hardy G, Littlewood J, Polya G. Inequalities [ M ]. Cambridge : Cambridge University Press, 1988 : 239-243.
  • 2Egnell H. Elliptic boundary value problems with singular coefficients and critical nonlinearities [ J ]. Indiana Univ Math, 1989, 38(2): 235-251.
  • 3Talenti G. Best constant in Sobolev inequality [ J ]. Ann Mat Pura Appl, 1976, 110(1) : 353-372.
  • 4Terracini S. On positive solutions to a class of equations with a singular coefficient and critical exponent [ J ]. Adv Differential Equations , 1996, 2(2) : 241-264.
  • 5Huang Y, Kang D. On the singular elliptic systems involving multiple critical Sobolev exponents [ J ]. Nonlinear Anal, 2011, 74( 1 ): 400-412.
  • 6Cao D, Han P. Solutions for semilinear elliptic equations with critical exponents and Hardy potential [ J ]. J Differential Equations, 2004, 205 ( 1 ) : 521-537.
  • 7Ferrero A, Gazzola F. Existence of solutions for singular critical growth semilinear elliptic equations [ J ]. J Differential Equations, 2001, 177 ( 1 ) : 494-522.
  • 8Rabinowitz P. Minimax methods in critical points theory with applications to differential Equations [ M ]. Washington : American Mathematical Society, 1986 : 7-50.

引证文献1

中南民族大学学报（自然科学版）
2013年 第1期

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