Recently, Ricceri posed a question about the uniqueness of a parameter such that a corresponding functional 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 parameters such that the above situation occurs.
A note on a question of Ricceri
IANNIZZOTTO, ANTONIO
2012-01-01
Abstract
Recently, Ricceri posed a question about the uniqueness of a parameter such that a corresponding functional 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 parameters such that the above situation occurs.
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