Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blow-up

In this paper we prove uniqueness of positive solutions to logistic singular problems -Deltau = lambda (x)u - a(x)u(p), u(\)partial derivative Omega = +infinity, p >1, a > 0 in Omega, where the main feature is the fact that a(\)partial derivative Omega = 0. More importantly, we provide exact asymptotic estimates describing, in the form of a two-term expansion, the blow-up rate for the solutions near partial derivative Omega. This expansion involves both the distance function d(x) = dist(x, partial derivative Omega) and the mean curvature H of partial derivative Omega.