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Theorems of existence and multiplicity for nonlinear elliptic problems with noninvertible linear part. (English) Zbl 0375.35024

MSC:
35J60 Nonlinear elliptic equations
47J05 Equations involving nonlinear operators (general)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35P05 General topics in linear spectral theory for PDEs
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References:
[1] A. Ambrosetti - G. Mancini , Existence and multiplicity results for nonlinear elliptic problems with linear part at resonance , to appear on J. Diff. Eq. [2] P.H. Rabinowitz , Some minimax theorems and applications to nonlinear partial differential equations , to appear. MR 501092 | Zbl 0466.58015 · Zbl 0466.58015
[2] S Fučik - M. Krbeč , Boundary value problems with bounded nonlinearity and general null space of the linear part , to appear on Math. Z. Article | MR 473513 | Zbl 0337.35034 · Zbl 0337.35034
[3] P. Hess , A remark on a preceding paper of Fučik and Krbeč , to appear on Math. Z. Article | MR 473514 | Zbl 0356.35030 · Zbl 0356.35030
[4] J.T. Schwartz , Nonlinear functional analysis , Gordon and Breach Intersc. Publ. ( 1969 ). MR 433481 | Zbl 0203.14501 · Zbl 0203.14501
[5] S. Ahmad - A.C. Lazer - J.L. Paul , Elementary critical point theory and perturbation of elliptic boundary value problems at resonance , Indiana Univ. Math. J. , 25 ( 1976 ), pp. 933 - 944 . MR 427825 | Zbl 0351.35036 · Zbl 0351.35036
[6] A. Ambrosetti , On the existence of multiple solutions for a class of nonlinear boundary value problems , Rend. Sem. Mat. Univ. Padova , 49 ( 1973 ), pp. 195 - 204 . Numdam | MR 336068 | Zbl 0273.35037 · Zbl 0273.35037
[7] E.N. Dancer , On a nonlinear elliptic boundary value problem , Bull. Australian Math. Soc. , 12 ( 1975 ), pp. 399 - 405 . MR 385318 | Zbl 0297.35031 · Zbl 0297.35031
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