Some remarks on a three critical points theorem (Q1399945)
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scientific article; zbMATH DE number 1957310
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some remarks on a three critical points theorem |
scientific article; zbMATH DE number 1957310 |
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Some remarks on a three critical points theorem (English)
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30 July 2003
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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.
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critical point
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minimax inequality
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elliptic eigenvalue problem
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two point boundary value problem
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Neumann problem
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