Boundary blow-up solutions of cooperative systems

We study the existence, uniqueness and boundary profile of nonnegative boundary blow-up solution to the cooperative system{Δu=g(u−v)in Ω,Δv=f(v−βu)in Ω,u=v=∞on ∂Ω in a smooth bounded domain of RNRN, where f, g   are nondecreasing, nonnegative C1C1 functions vanishing in (−∞,0](−∞,0] and β>0β>0 is a parameter.