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.
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania
Critical point; extremum point; Palais-Smale condition; two-point boundary value problem
R. Precup, On a bounded critical point theorem of Schechter, Stud. Univ. Babeş-Bolyai Math. 58 (2013) no. 1, 87-95.
Studia Universitatis Babes-Bolyai Mathematica
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