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含Hardy位势的双调和方程特征值问题 被引量：5

Eigenvalue problems of bi-harmonic equations with Hardy potential
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摘要 对于一类包含Hardy位势1/|x|4(N≥5)的双调和方程的特征值问题,通过建立一个新空间和一个Hardy-Rellich不等式证明该特征值问题的解的存在性。 The eigenvalue problem of bi-harmonic equations with Hardy potential 1/ ｜x｜ ^4 （ N ≥ 5） was investigated based on an establishment of a new space and a flardy-Rellich inequality. Furthermore, the results show the solvability of these problems in the new space.
作者 伍芸 姚仰新 柯敏
机构地区 贵州师范大学数学与计算机科学学院 华南理工大学数学科学学院
出处 《山东大学学报（理学版）》 CAS CSCD 北大核心 2008年第9期81-84,共4页 Journal of Shandong University(Natural Science)
基金 国家自然科学基金资助项目(10771074)
关键词 特征值问题 双调和方程 HARDY位势 eigenvalue problem bi-harmonic equation Hardy potential
分类号 O175.25 [理学—基础数学]
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二级参考文献12

  • 1Shen, Y.T. On the Dirichlet problem for quasilinear elliptic equation with strongly singular coefficients.Proc. of the 1980 Beijing symp. on Diff. Geom. and Diff. Equation, Science Press, Gordon and Breach Science Publishers, 3:1407-1417 (1982).
  • 2Shen, Y.T. Weak'solutions of ell'iptic "equations of second order with singular coefficients. Advances in Mathematics, 7:321-327 (1964) (in Chinese).
  • 3Talenti, G. Elliptic equations and rearrangements. Ann. Scuola Norm. Sup. Pisa. CI. Sci., Ser. IV, 3:697-718 (1976).
  • 4Adimurthi, Chaudhuri N., Ramaswamy, M. An improved Hardy-Sobolev inequality and its application.Proc. Amer, Math. Soc,, 130:489-505 (2002).
  • 5Almgren, F,, Lieb, E. Symmetric decreasing rearrangement is sometimes continuous. J. Amer, Math.Soc,, 2:683-773 (1989).
  • 6Brezis, H,, Lieb, E. A relation between point convergence of functions and convergence of functionals.Proc, Amer, Math, Soc,, 88:486-490 (1983).
  • 7Brezis, H,, Vazquez J,L. Blow-up solution of some nonlinear elliptic equation. Rev, Mat. Complut., 10(2):443-469 (1997).
  • 8Chaudhuri, N," Existence of positive solutions of some semilinear elliptic equations with singular coefficients,Proc, Roy. Soc. Edinburgh Sec, A, 131:1275-1295 (2001).
  • 9Dold, J.W., Galaktionov,VV,A., Lacey, A.A,, Vazquez, J.L. Rate of approach to a singular steady state in quasilinear reaction-diffusion equations. Ann, Scuola Noem, Sup. CI, Sci,. 26(4): 663-687 (1998).
  • 10Ekeland I. On the variational priciple. J. Math, Anal, Appl.. 47:324- 353 (1974).

共引文献12

同被引文献16

  • 1陈志辉,沈尧天,姚仰新.R^4中含位势的非线性双调和方程[J].数学年刊（A辑）,2005,26(4):487-494. 被引量：7
  • 2Gazzola F.Grunau H F.Mitidieri E.Hardy inequalities with optimal constants and remainders[J].Trans Amer Math Soc,2004(6):2168-2419.
  • 3Adimurthi,Chaudhuri N.Ramaswamy M,et al.Optimal Hardy-Rellich inequalities,maximum principle and related eigenvalue problem its applications[J].Journal of Functional Analysis,2006,240:36-83.
  • 4Ambrosetti A.Rabinowitz P H.Dual variational method in critical point theory and applications[J].J Functional Anal,1973,14:349-381.
  • 5Adimurthi M.G,Sanjiban S.Optimal Hardy-Rellich inequalities,maximum principle and related eigenvalue problem. Journal of Functional Analysis . 2006
  • 6Yu K,Liu R.Y.Existence of nontrivial solutions of an asymptotically linear fourth-order elliptic equation. Nonlinear Analysis . 2008
  • 7F. Gazzola,H.-C. Grunau,E. Mitidieri.Hardy inequalities with optimal constants and remainder terms. Transactions of the American Mathematical Society . 2004
  • 8Tertikas A,Zongraphopoulos N B.Best constants in Har-dy-Rellich inequalities and related improve-ments. Advances in Mathematics . 2007
  • 9陈志辉,沈尧天.含距离位势的拟线性椭圆方程解的存在性[J].数学学报（中文版）,2008,51(3):469-474. 被引量：3
  • 10祁瑞改,杨国英.用山路引理证明拟线性方程组正解的存在性[J].郑州大学学报（理学版）,2010,42(3):19-22. 被引量：2

引证文献5

二级引证文献9

山东大学学报（理学版）
2008年 第9期

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