## 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

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