Boundary blow-up solutions for a cooperative system of quasilinear equation

We study the existence, uniqueness and boundary behavior of positive boundary blow-up solutions to the quasilinear elliptic system{Δpu=w(x)ua/vbin Ω,Δpv=λ(x)vc/uein Ω,u=v=∞on ∂Ω in a smooth bounded domain Ω⊂RNΩ⊂RN. The operator ΔpΔp stands for the p-Laplacian defined by Δpu=div(|∇u|p−2∇u)Δpu=div(|∇u|p−2∇u), p>1p>1, the exponents a, b, c, e   verify a,c>p−1a,c>p−1, b,e>0b,e>0, and the weight functions w(x)w(x), λ(x)λ(x) are positive and may blow up on the boundary ∂Ω.