On a bounded critical point theorem of Schechter


A new proof based on Bishop-Phelps’ variational principle is given to a critical point theorem of Schechter for extrema in a ball of a Hilbert space. The same technique is used to obtain a similar result in annular domains. Comments on the involved boundary conditions and an application to a two-point boundary value problem are included. An alternative variational approach to the compression-expansion Krasnoselskii’s fixed point method is thus provided. In addition, estimations from below are obtained here for the first time, in terms of  the energetic norm.


Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania


Critical point; extremum point; Palais-Smale condition; two-point boundary value problem

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R. Precup, On a bounded critical point theorem of Schechter, Stud. Univ. Babeş-Bolyai Math. 58 (2013) no. 1, 87-95.


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Studia Universitatis Babes-Bolyai Mathematica

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“Babeș-Bolyai” University

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