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 Khalil1
, Siham Kellati2
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
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.