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We show the existence of at least one nontrivial solution of the homogeneous mixed type nonlinear elliptic problem. Here mixed type nonlinearity means that the nonlinear part contain the jumping nonlinearity and the critical growth nonlinearity. We first investigate the sub-level sets of the corresponding functional in the Soboles space and the linking inequalities of the functional on the sub-level sets. We next investigate that the functional I satisfies the mountain pass geometry in the critical point theory. We obtain the result by the mountain pass method, the critical point theory and variational method.
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참고문헌 (11)
참고문헌 신청
A. Castro / 1979 / Critical point theory and the number of solutions of a nonlinear Dirichlet problem / Ann. Mat. Pura Appl 120 (4) : 113 ~ 137
A. Castro / 1994 / Multiple Solutions for a nonlinear Dirichlet problem / SIAM J. Math. Anal 25 (6) : 1554 ~ 1561
A. Groli / 1998 / Variational theorems of mixed type and asymptotically linear variational inequalities / Topological Methods in Nonlin-ear Analysis 12 : 109 ~ 136
A. M. Micheletti / 1998 / Multiplicity results for a fourth-order semilinear elliptic problem / Nonlinear Analysis, TMA 31 (7) : 895 ~ 908
A. Marino / 1997 / Some variational theorems of mixed type and elliptic problems with jumping nonlinearities / Ann. Scuola Norm (Sup) : 631 ~ 665
A. Castro / 1994 / Multiple Solutions for a nonlinear Dirichlet problem / SIAM J. Math. Anal 25 (6) : 1554 ~ 1561
A. Groli / 1998 / Variational theorems of mixed type and asymptotically linear variational inequalities / Topological Methods in Nonlin-ear Analysis 12 : 109 ~ 136
A. M. Micheletti / 1998 / Multiplicity results for a fourth-order semilinear elliptic problem / Nonlinear Analysis, TMA 31 (7) : 895 ~ 908
A. Marino / 1997 / Some variational theorems of mixed type and elliptic problems with jumping nonlinearities / Ann. Scuola Norm (Sup) : 631 ~ 665
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