Korean Journal of Mathematics

  • 제18권3호
  • /
  • Pages.323-334
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  • 2010
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  • 1976-8605(pISSN)
  • /
  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
권호 표지

FOURTH ORDER ELLIPTIC BOUNDARY VALUE PROBLEM WITH SQUARE GROWTH NONLINEARITY

  • Jung, Tacksun (Department of Mathematics Kunsan National University) ;
  • Choi, Q-Heung (Department of Mathematics Education Inha University)
  • 투고 : 2010.09.01
  • 심사 : 2010.09.15
  • 발행 : 2010.09.30
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초록

We give a theorem for the existence of at least three solutions for the fourth order elliptic boundary value problem with the square growth variable coefficient nonlinear term. We use the variational reduction method and the critical point theory for the associated functional on the finite dimensional subspace to prove our main result. We investigate the shape of the graph of the associated functional on the finite dimensional subspace, (P.S.) condition and the behavior of the associated functional in the neighborhood of the origin on the finite dimensional reduction subspace.

키워드

참고문헌

  1. Choi, Q. H. and Jung, T., Multiplicity of solutions and source terms in a fourth order nonlinear elliptic equation, Acta Math. Sci. 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. 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. 31(7)(1998), 895-908. https://doi.org/10.1016/S0362-546X(97)00446-X
  5. Rabinowitz and P. H.,Minimax methods in critical point theory with applica- tions to differential equations, CBMS. Regional conf. Ser. Math. 65, Amer. Math. Soc., Providence, Rhode Island, 1986.
  6. Tarantello, A note on a semilinear elliptic problem, Differ. Integral. Equ. Appl. 5(3)(1992), 561-565.