Abstract
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.
Authors
Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
Critical point; extremum point; Palais-Smale condition; two-point boundary value problem
Paper coordinates
R. Precup, On a bounded critical point theorem of Schechter, Stud. Univ. Babeş-Bolyai Math. 58 (2013) no. 1, 87-95.
About this paper
Journal
Studia Universitatis Babes-Bolyai Mathematica
Publisher Name
“Babeș-Bolyai” University
Print ISSN
Online ISSN
0370-8659
google scholar link
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