Asymptotics for the blow-up boundary solution of the logistic equation with absorption

Let Omega be a smooth bounded domain in R-N. Assume that f greater than or equal to 0 is a C-1-function on [0, infinity) such that f (u)/u is increasing on (0, +infinity). Let a be a real number and let b greater than or equal to, 0, b not equivalent to 0 be a continuous function such that b = 0 on partial derivativeOmega. The purpose of this Note is to establish the asymptotic behaviour of the unique positive solution of the logistic problem Deltan + au = b(x)f (u) in Omega, subject to the singular boundary condition u(x) --> +infinity as dist(x, partial derivativeOmega) --> 0. Our analysis is based on the Karamata regular variation theory.