Korean Journal of Mathematics

  • 제18권2호
  • /
  • Pages.201-211
  • /
  • 2010
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  • 1976-8605(pISSN)
  • /
  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
권호 표지

NUMBER OF THE NONTRIVIAL SOLUTIONS OF THE NONLINEAR BIHARMONIC PROBLEM

  • Jung, Tacksun (Department of Mathematics Kunsan National University) ;
  • Choi, Q-Heung (Department of Mathematics Education Inha University)
  • 투고 : 2010.05.12
  • 심사 : 2010.06.10
  • 발행 : 2010.06.30
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초록

We investigate the number of the nontrivial solutions of the nonlinear biharmonic equation with Dirichlet boundary condition. We give a theorem that there exist at least three nontrivial solutions for the nonlinear biharmonic problem. We prove this result by the finite dimensional reduction method and the shape of the graph of the corresponding functional on the finite reduction subspace.

키워드

과제정보

연구 과제 주관 기관 : Inha University

참고문헌

  1. Choi, Q. H. and Jung, T., Multiplicity of solutions and source terms in a fourth order nonlinear elliptic equation, Acta Math. Sinica (Chin. Ser.), 19(4)(1999), 361-374.
  2. Choi, Q. H. and Jung, T., Multiplicity results on nonlinear biharmonic operator, Rocky Mountain J. Math. 29(1)(1999), 141-164. https://doi.org/10.1216/rmjm/1181071683
  3. Jung, T. S. and Choi, Q. H., Multiplicity results on a nonlinear biharmonic equation, Nonlinear Anal., TMA, 30(8)(1997), 5083-5092. https://doi.org/10.1016/S0362-546X(97)00381-7
  4. Micheletti, A. M. and Pistoia, A., Multiplicity results for a fourth-order semi- linear elliptic problem, Nonlinear Anal., TMA, 31(7)(1998), 895-908. https://doi.org/10.1016/S0362-546X(97)00446-X
  5. Tarantello, A note on a semilinear elliptic problem, Differ. Integral Equ. Appl., 5(3)(1992), 561-565.