Uniqueness of positive solutions for a boundary blow-up problem

AbstractIn 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 C2 bounded domain in RN, under the hypotheses that f(t) is nondecreasing in t>0 and f(t)/tp is increasing for large t and some p>1. We also consider the uniqueness of a related problem when the equation includes a nonnegative weight a(x)