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Zbl 1031.49006
Bonanno, Gabriele
Some remarks on a three critical points theorem. (English)
[J] Nonlinear Anal., Theory Methods Appl. 54, No.4, A, 651-665 (2003). ISSN 0362-546X

This paper establishes several applications to nonlinear boundary value problems of the three critical points theorem of Ricceri. First, the author proves several abstract results related to a strict minimax inequality. As applications, there are established multiplicity results for nonlinear elliptic problems, including: (i) a two-point boundary value problem, (ii) a Dirichlet problem for semilinear elliptic equations with discontinuous nonlinearities, and (iii) a nonlinear Neumann boundary problem. The proofs rely on refined arguments in the critical point theory.
[Vicenţiu D.Rădulescu (Craiova)]

MSC 2000:: *49J35 Minimax problems (existence)
35B38 Critical points
34B15 Nonlinear boundary value problems of ODE
35J65 (Nonlinear) BVP for (non)linear elliptic equations
35R05 PDE with discontinuous coefficients or data
58E05 Abstract critical point theory

Keywords: critical point; minimax inequality; elliptic eigenvalue problem; two point boundary value problem; Neumann problem

Cited in: Zbl 1248.35072 Zbl 1234.34016 Zbl pre06150134 Zbl 1183.35154 Zbl 1188.49007 Zbl 1181.35162 Zbl 1173.35490 Zbl 1159.35352 Zbl 1136.35034 Zbl 1065.49014 Zbl 1087.58007

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