Uniqueness of positive solutions for a boundary blow-up problem

Abstract

In this paper we prove the uniqueness of the positive solution for the boundary blow-up problem{(Δ u = 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). © 2009 Elsevier Inc. All rights reserved.