At least two solutions for the semilinear biharmonic boundary value problem
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초록
We get one theorem that there exists a unique solution for the fourth order semilinear elliptic Dirichlet boundary value problem when the number 0 and the coefficient of the semilinear part belong to the same open interval made by two successive eigenvalues of the fourth order elliptic eigenvalue problem. We prove this result by the contraction mapping principle. We also get another theorem that there exist at least two solutions when there exist n eigenvalues of the fourth order elliptic eigenvalue problem between the coefficient of the semilinear part and the number 0. We prove this result by the critical point theory and the variation of linking method.
Abstract
We get one theorem that there exists a unique solution for the fourth order semilinear elliptic Dirichlet boundary value problem when the number 0 and the coefficient of the semilinear part belong to the same open interval made by two successive eigenvalues of the fourth order elliptic eigenvalue problem. We prove this result by the contraction mapping principle. We also get another theorem that there exist at least two solutions when there exist n eigenvalues of the fourth order elliptic eigenvalue problem between the coefficient of the semilinear part and the number 0. We prove this result by the critical point theory and the variation of linking method.
참고문헌 (10)
- Chang, k. C., "Infinite dimensional Morse theory and multiple solution problems" (1993), Birkhauser
- Choi, Q. H., "Multiplicity of solutions and source terms in a fourth order nonlinear elliptic equation", Acta Mathematica Scientia, 19(4), pp.361~374 (1999)
- Choi, Q. H., "Multiplicity results on nonlinear biharmonic operator", Rocky Mountain J. Math, 29(1), pp.141~164 (1999)
- Choi, Q. H., "An application of a variational reduction method to a nonlinear wave equation", J. Differential Equations, 7, pp.390~410 (1995)
- Jung, T. S., "Multiplicity results on a nonlinear biharmonic equation", Nonlinear Analysis, Theory, Methods and Applications, 30(8), pp.5083~5092 (1997)
- Lazer, A. C., "Multiplicity results for a class of semilinear elliptic and parabolic boundary value problems", J. Math. Anal. Appl, 107, pp.371~395 (1985)
- McKenna, P. J., "On the multiplicity of the solution set of some nonlinear boundary value problems, Nonlinear Analysis", Theory, Methods and Applications, 8, pp.893~907 (1984)
- Micheletti, A. M., "Multiplicity results for a fourth-order semi-linear elliptic problem", Nonlinear Analysis TMA, 31(7), pp.895~908 (1998)
- Rabinowitz, P. H., "Minimax methods in critical point theory with applications to differential equations", CBMS. Regional conf. Ser. Math., 65 (1986), Amer. Math. Soc.
- Tarantello, "A note on a semilinear elliptic problem", Diff. Integ. Equat, 5(3), pp.561~565 (1992)