We consider the nonlinear eigenvalue problem −div(∣∇u∣p(x)−2∇u)=λ∣u∣q(x)−2u in Ω, u=0 on
∂Ω, where Ω is a bounded open set in \RR^N with smooth
boundary and p, q are continuous functions on Ωˉ such that
1<inf_Ωq<inf_Ωp<sup_Ωq, sup_Ωp<N, and
q(x)<Np(x)/(N−p(x)) for all x∈Ωˉ. The main result of this paper
establishes that any λ>0 sufficiently small is an eigenvalue of the
above nonhomogeneous quasilinear problem. The proof relies on simple
variational arguments based on Ekeland's variational principle