We study through the lower and upper-solution method, the existence of positive weak solution to the
quasilinear elliptic system with weights
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−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.
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