Uniqueness and layer analysis for boundary blow-up solutions

We prove uniqueness for boundary blow-up solutions of the problem: Deltau = lambdaf(u) in Omega, u\partial derivativeOmega = infinity, with large lambda. Previous uniqueness results require a monotonicity assumption for f (u)/u in the entire range of the boundary blow-up solutions. By obtaining good boundary layer estimates for large lambda, we obtain uniqueness under much weaker assumptions on f (u). Our estimates for the layers of the boundary blow-up solutions have independent interest, and may have other applications. (C) 2004 Elsevier SAS. All rights reserved.