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+c1uαvγinΩ,−div(|x|−bq|∇v|q−2∇v)=λ|x|−(b+1)q+c2uδvβinΩ,u=v=0on ∂Ω, where Ω   is a bounded smooth domain of RNRN, with 0∈Ω0∈Ω, 10δ,γ,c1,c2>0 and θ:=(p−1−α)(q−1−β)−γδ>0θ:=(p−1−α)(q−1−β)−γδ>0, for each λ>0λ>0.