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 { Δ p u = w ( x ) u a / v b in Ω , Δ p v = λ ( x ) v c / u e in Ω , u = v = ∞ on ∂ Ω in a smooth bounded domain Ω ⊂ R N . The operator Δ p stands for the p-Laplacian defined by Δ p u = div ( | ∇ u | p − 2 ∇ u ) , p > 1 , the exponents a, b, c, e verify a , c > p − 1 , b , e > 0 , and the weight functions w ( x ) , λ ( x ) are positive and may blow up on the boundary ∂Ω.