Boundary blow-up in nonlinear elliptic equations of bieberbach-rademacher type

We establish the uniqueness of the positive solution for equations of the form -δu = au - b(x)f(u) in ω, u|∂ω = ∞. The special feature is to consider nonlinearities f whose variation at infinity is not regular (e.g., exp(u) - 1, sinh(u), cosh(u) - 1, exp(u) log(u + 1), u ^β exp(u^γ), β ε ℝ, γ > 0 or exp(exp(u)) - e) and functions b ≥ 0 in O vanishing on ∂ω. The main innovation consists of using Karamata's theory not only in the statement/proof of the main result but also to link the nonregular variation of f at infinity with the blow-up rate of the solution near ∂ω.