Applied Mathematics and Mechanics

, Volume 16, Issue 7, pp 687–694 | Cite as

Infinitely many solutions for double hamonic perturbed problem

  • Dai Qiuyi


In this paper we consider the double hamonic perturbed problem on a bounded domain frith boundary-value zero. The results which we have obtained have improved the results obtained in [1], [3] and [4].

Key words

double hamonic operator generalized Morse indice nontrivial solution 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. Bahri and H. Berestycki, A perturbation method in critical point theory and applications,Trans A. M. S. 267, 1 (1981), 1–32.zbMATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    A. Bahri and H. Berestycki, Forced vibrations of superquadratic-Hamiltonian system,Acta Math.,152, 3-4 (1984), 143–197.zbMATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    Dai Shuhuan and Nain Ziqian, The existence of the nontrivial solution of the equation Δ2 u -aΔu+bu = ƒ(x, u)-an application of the mountain pass lemms,J. Jilin University,1 (1984). (in Chinese)Google Scholar
  4. [4]
    Tang Xianjiang, Infinitely solutions of the equation Δ2 u-aΔu+bu=ƒ(x, u)+g(x, u)J. Shichuan University, 4 (1984). (in Chinese)Google Scholar
  5. [5]
    S. T. Yau,Differential Geometry, Science Press (1988). (in Chinese)Google Scholar
  6. [6]
    Dai Qiuyi, The estimation of the nonpositive eigenvalues for operator Δ2-v(x) and application,ACTA MA THEMA TICA SCIENTIA, 12 (1992), 93–95. (in Chinese)Google Scholar
  7. [7]
    P. Li and S. T. Yau, On the Schrödinger Equation and the eigenvalue problem,Comm. Math. Phy.,88 (1982), 309–318.MathSciNetCrossRefGoogle Scholar
  8. [8]
    Kazunaga Tanaka, Morse indices at critical points related to the symmetric mountain pass theorem and applications,Comm P. D. E.,14, 1 (1989), 99–128.zbMATHGoogle Scholar
  9. [9]
    Chang Kungching,Critical Point Theory and Its Applications, Shanghai Science and Technolagy Press (1986). (in Chinese)Google Scholar
  10. [10]
    Lian Shantao and Liu Jinwang, {btFundaments of Homotopy Theory}, Beijing University Press (1980). (in Chinese)Google Scholar
  11. [11]
    P. H. Rabinowitz, Course Lecture-CIME. Varenna Italy (1974).Google Scholar
  12. [12]
    R. S. Palais, Morse theory on Hilbert manifolds,Topology, 2 (1963), 299–340.Google Scholar

Copyright information

© Shanghai University of Technology (SUT) 1995

Authors and Affiliations

  • Dai Qiuyi
    • 1
  1. 1.Xiangtan Mining InstituteXiangtanP. R. China

Personalised recommendations