Abstract and Applied Analysis
Volume 2012 (2012), Article ID 434631, 9 pages
http://dx.doi.org/10.1155/2012/434631
Research Article

On the Variational Eigenvalues Which Are Not of Ljusternik-Schnirelmann Type

Pavel Drábek

Department of Mathematics and N.T.I.S., University of West Bohemia, Univerzitní 22, 306 14 Plzeň, Czech Republic

Received 29 November 2011; Revised 12 January 2012; Accepted 12 January 2012

Academic Editor: Donal O'Regan

Copyright © 2012 Pavel Drábek. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We discuss nonlinear homogeneous eigenvalue problems and the variational characterization of their eigenvalues. We focus on the Ljusternik-Schnirelmann method, present one possible alternative to this method and compare it with the Courant-Fischer minimax principle in the linear case. At the end we present a special nonlinear eigenvalue problem possessing an eigenvalue which allows the variational characterization but is not of Ljusternik-Schnirelmann type.