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EIGENVALUE PROBLEM OF BIHARMONIC EQUATION WITH HARDY POTENTIAL

  • Yao, Yangxin (DEPARTMENT OF MATHEMATICS SOUTH CHINA UNIVERSITY OF TECHNOLOGY) ;
  • He, Shaotong (DEPARTMENT OF MATHEMATICS SOUTH CHINA UNIVERSITY OF TECHNOLOGY) ;
  • Su, Qingtang (SCHOOL OF MATHEMATICS AND COMPUTATIONAL SCIENCE SUN YAT-SEN UNIVERSITY)
  • Received : 2008.12.25
  • Published : 2010.11.01

Abstract

In this paper, we consider the eigenvalue problem of biharmonic equation with Hardy potential. We improve the results of references by introducing a new Hilbert space.

Keywords

References

  1. R. A. Adams, Sobolev Spaces, Academic Press, New York-London, 1975.
  2. Adimurthi, M. Grossi, and S. Santra, Optimal Hardy-Rellich inequalities, maximum principle and related eigenvalue problem, J. Funct. Anal. 240 (2006), no. 1, 36-83. https://doi.org/10.1016/j.jfa.2006.07.011
  3. I. Ekeland, On the variational principle, J. Math. Anal. Appl. 47 (1974), 324-353. https://doi.org/10.1016/0022-247X(74)90025-0
  4. S. Filippas and A. Tertikas, Optimizing improved Hardy inequalities, J. Funct. Anal. 192 (2002), no. 1, 186-233. https://doi.org/10.1006/jfan.2001.3900
  5. F. Gazzola, H. C. Grunau, and E. Mitidieri, Hardy inequalities with optimal constants and remainder terms, Trans. Amer. Math. Soc. 356 (2004), no. 6, 2149-2168. https://doi.org/10.1090/S0002-9947-03-03395-6
  6. A. Tertikas and N. B. Zographopolous, Best constants in the Hardy-Rellich inequalities and related improvements, Adv. Math. 209 (2007), no. 2, 407-459. https://doi.org/10.1016/j.aim.2006.05.011
  7. M. Willem, Minimax Theorems, Birkhauser Boston, Inc., Boston, MA, 1996.
  8. Y. X. Yao, Y. T. Shen, and Z. H. Chen, Biharmonic equation and an improved Hardy inequality, Acta Math. Appl. Sin. Engl. Ser. 20 (2004), no. 3, 433-440. https://doi.org/10.1007/s10255-004-0182-y