Uniqueness of positive solutions for a boundary blow-up problem

In this paper we prove the uniqueness of the positive solution for the boundary blow-up problem{Δu=f(u)in Ω,u=∞on ∂Ω, where Ω   is a C2C2 bounded domain in RNRN, under the hypotheses that f(t)f(t) is nondecreasing in t>0t>0 and f(t)/tpf(t)/tp is increasing for large t   and some p>1p>1. We also consider the uniqueness of a related problem when the equation includes a nonnegative weight a(x)a(x).