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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.
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참고문헌 (6)
참고문헌 신청
Choi, Q. H. / 1999 / Multiplicity of solutions and source terms in a fourth order nonlinear elliptic equation / Acta Math. Sci. 19 (4) : 361 ~ 374
Choi, Q. H. / 1999 / Multiplicity results on nonlinear biharmonic opera-tor / Rocky Mountain J. Math. 29 (1) : 141 ~ 164
Jung, T. S. / 1997 / Multiplicity results on a nonlinear biharmonic equation / Nonlinear Anal. 30 (8) : 5083 ~ 5092
Micheletti, A. M. / 1998 / Multiplicity results for a fourth-order semi-linear elliptic problem / Nonlinear Anal. 31 (7) : 895 ~ 908
Rabinowitz and P. H. / 1986 / Minimax methods in critical point theory with applica-tions to differential equations / CBMS. Regional conf. Ser. Math.
Choi, Q. H. / 1999 / Multiplicity results on nonlinear biharmonic opera-tor / Rocky Mountain J. Math. 29 (1) : 141 ~ 164
Jung, T. S. / 1997 / Multiplicity results on a nonlinear biharmonic equation / Nonlinear Anal. 30 (8) : 5083 ~ 5092
Micheletti, A. M. / 1998 / Multiplicity results for a fourth-order semi-linear elliptic problem / Nonlinear Anal. 31 (7) : 895 ~ 908
Rabinowitz and P. H. / 1986 / Minimax methods in critical point theory with applica-tions to differential equations / CBMS. Regional conf. Ser. Math.
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