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