Some remarks on a three critical points theorem. (English) Zbl 1031.49006
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.
Reviewer: Vicenţiu D.Rădulescu (Craiova)
MSC:
| 49J35 | Existence of solutions for minimax problems |
| 35B38 | Critical points of functionals in context of PDEs (e.g., energy functionals) |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 35J65 | Nonlinear boundary value problems for linear elliptic equations |
| 35R05 | PDEs with low regular coefficients and/or low regular data |
| 58E05 | Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces |
Keywords:
critical point; minimax inequality; elliptic eigenvalue problem; two point boundary value problem; Neumann problemReferences:
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