Table of Contents
International Journal of Analysis
Volume 2014, Article ID 498386, 8 pages
http://dx.doi.org/10.1155/2014/498386
Research Article

On the -Biharmonic Operator with Critical Sobolev Exponent and Nonlinear Steklov Boundary Condition

1Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh 11623, Saudi Arabia
2Department of Mathematics, Faculty of Sciences Dhar-Mahraz, University Sidi Mohamed Ben Abdellah, P.O. Box 1796, Atlas-Fez, Fez 30000, Morocco

Received 26 November 2013; Accepted 30 January 2014; Published 19 March 2014

Academic Editor: Patrick Guidotti

Copyright © 2014 Abdelouahed El Khalil et al. 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 show that this operator possesses at least one nondecreasing sequence of positive eigenvalues. A direct characterization of the principal eigenvalue (the first one) is given that we apply to study the spectrum of the -biharmonic operator with a critical Sobolev exponent and the nonlinear Steklov boundary conditions using variational arguments and trace critical Sobolev embedding.