A note on a question of Ricceri

IANNIZZOTTO, ANTONIO;Cabada, A.

2012-01-01

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Abstract

Recently, Ricceri posed a question about the uniqueness of a parameter lambda such that a certain functional depending on lambda admits at least three critical points in a finite-dimensional Hilbert space X (under certain assumptions on the functional). We give the answer, which is negative, even in the case of infinite-dimensional spaces. Moreover, we discuss the structure of the set of lambda's such that the above situation occurs.