## 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

### Keywords:

critical points; semilinear Dirichlet problem
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