Number of the nontrivial solutions of the nonlinear biharmonic problem
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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.
Abstract
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.
참고문헌 (5)
- Choi, Q. H., "Multiplicity of solutions and source terms in a fourth order nonlinear elliptic equation", Acta Math. Sinica (Chin. Ser.), 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)
- Jung, T. S., "Multiplicity results on a nonlinear biharmonic equation", Nonlinear Anal., TMA, 30(8), pp.5083~5092 (1997)
- Micheletti, A. M., "Multiplicity results for a fourth-order semi-linear elliptic problem", Nonlinear Anal., TMA, 31(7), pp.895~908 (1998)
- Tarantello, "A note on a semilinear elliptic problem", Differ. Integral Equ. Appl., 5(3), pp.561~565 (1992)