Simplicity and stability of the first eigenvalue of a nonlinear elliptic system
Abdelouahed El Khalil,1Said El Manouni,2,3and Mohammed Ouanan3
Received08 Jul 2004
Revised17 Mar 2005
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.