International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 10, Pages 1555-1563
doi:10.1155/IJMMS.2005.1555
Simplicity and stability of the first eigenvalue of a nonlinear elliptic system
Abdelouahed El Khalil1
, Said El Manouni2
and Mohammed Ouanan3
1Département de Mathématiques et Génie Industriel, Ecole Polytechnique de Montréal, H3C 3A7, Canada
223 Biesentaler Street, Berlin 13359, Germany
3Department of Mathematics, Faculty of Sciences Dhar-Mahraz, P.O. Box 1796 Atlas, Fez 30000, Morocco
Abstract
We prove some properties of the first eigenvalue for the elliptic system −Δpu=λ|u|α|v|βv in Ω, −Δqv=λ|u|α|v|βu in Ω, (u,v)∈W01,p(Ω)×W01,q(Ω). In particular, the first eigenvalue is shown to be simple. Moreover, the stability with respect to (p,q) is established.