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On a three critical points theorem. (English) Zbl 0979.35040

The author consider a smooth functional depending on a real parameter \(\lambda\). He obtains certain results on existence of an open interval of \(\lambda\)’s for which there exist at least three critical points. An application to a semilinear Dirichlet problem is mentioned.

MSC:

35J20 Variational methods for second-order elliptic equations
49J35 Existence of solutions for minimax problems
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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