On positive solutions for a class of singular quasilinear elliptic systems

We study through the lower and upper-solution method, the existence of positive weak solution to the quasilinear elliptic system with weights ⎧⎪ ⎨⎪ ⎩ −div(|x|−ap|∇u|p−2∇u) = λ|x|−(a+1)p+c1uαvγ in Ω, −div(|x|−bq|∇v|q−2∇v) = λ|x|−(b+1)q+c2uδvβ in Ω, u = v =0 on ∂Ω, where Ω is a bounded smooth domain of RN, with 0 ∈ Ω, 1 < p,q 0 and θ := (p −1−α)(q −1−β)−γ δ >0, for each λ>0. © 2007 Elsevier Inc. All rights reserved