International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 10, Pages 1525-1537
doi:10.1155/IJMMS.2005.1525

A nonlinear boundary problem involving the p-bilaplacian operator

Abdelouahed El Khalil,1 Siham Kellati,2 and Abdelfattah Touzani2

1Department of Mathematics and Industrial Engineering, Polytechnic School of Montreal, Montreal H3C 3A7, QC, Canada
2Department of Mathematics, Faculty of Sciences Dhar-Mahraz, University Sidi Med Ben Abdellah, P.O. Box 1796 Atlas, Fez 30000, Morocco

Received 8 January 2005; Revised 3 May 2005

Copyright © 2005 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 some new Sobolev's trace embedding that we apply to prove that the fourth-order nonlinear boundary conditions Δp2u+|u|p−2u=0 in Ω and −(∂/∂n)(|Δu|p−2Δu)=λρ|u|p−2u on ∂Ω possess at least one nondecreasing sequence of positive eigenvalues.