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

Ricceri, Biagio

Arch. Math. 75, No. 3, 220-226 (2000).

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.

Reviewer: Aleksander Pankov (Vinnitsa)

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

Keywords:

critical points; semilinear Dirichlet problem