Korean Journal of Mathematics

  • 제18권1호
  • /
  • Pages.87-96
  • /
  • 2010
  • /
  • 1976-8605(pISSN)
  • /
  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
권호 표지

REDUCTION METHOD APPLIED TO THE NONLINEAR BIHARMONIC PROBLEM

  • Jung, Tacksun (Department of Mathematics Kunsan National University) ;
  • Choi, Q-Heung (Department of Mathematics Education Inha University)
  • 투고 : 2010.01.11
  • 심사 : 2010.03.08
  • 발행 : 2010.03.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

We consider the semilinear biharmonic equation with Dirichlet boundary condition. We give a theorem that there exist at least three nontrivial solutions for the semilinear biharmonic boundary value problem. We show this result by using the critical point theory, the finite dimensional reduction method and the shape of the graph of the corresponding functional on the finite reduction subspace.

키워드

참고문헌

  1. Chang, K.C., Infinite dimensional Morse theory and multiple solution problems, Birkhauser, (1993).
  2. Choi, Q.H., Jung, T.S., Multiplicity of solutions and source terms in a fourth order nonlinear elliptic equation, Acta Mathematica Scientia, 19, No. 4, 361-374 (1999).
  3. Choi, Q.H., Jung, T.S., Multiplicity results on nonlinear biharmonic operator, Rocky Mountain J. Math. 29, No. 1, 141-164 (1999). https://doi.org/10.1216/rmjm/1181071683
  4. Choi, Q.H., Jung, T.S., An application of a variational reduction method to a nonlinear wave equation, J. Differential Equations 7, 390-410 (1995).
  5. Jung, T.S., Choi, Q.H., Multiplicity results on a nonlinear biharmonic equation, Nonlinear Analysis, Theory, Methods and Applications, 30, No. 8, 5083-5092 (1997). https://doi.org/10.1016/S0362-546X(97)00381-7
  6. Lazer, A.C., Mckenna, J.P., Multiplicity results for a class of semilinear elliptic and parabolic boundary value problems, J. Math. Anal. Appl., 107, 371-395 (1985). https://doi.org/10.1016/0022-247X(85)90320-8
  7. Micheletti, A.M., Pistoia, A., Multiplicity results for a fourth-order semilinear elliptic problem, Nonlinear Analysis, TMA, 31, No. 7, 895-908 (1998). https://doi.org/10.1016/S0362-546X(97)00446-X
  8. Rabinowitz, P.H., Minimax methods in critical point theory with applications to differential equations, CBMS. Regional conf. Ser. Math., 65, Amer. Math. Soc., Providence, Rhode Island (1986).
  9. Tarantello, A note on a semilinear elliptic problem, Diff. Integ.Equat., 5, No. 3, 561-565 (1992).