Asymptotics for the Blow-Up Boundary Solution of the Logistic Equation with Absorption

Abstract Let Ω be a smooth bounded domain in R N . Assume that f⩾0 is a C1-function on [0,∞) such that f(u)/u is increasing on (0,+∞). Let a be a real number and let b⩾0, b≢0 be a continuous function such that b≡0 on ∂Ω . The purpose of this Note is to establish the asymptotic behaviour of the unique positive solution of the logistic problem Δu+au=b(x)f(u) in  Ω , subject to the singular boundary condition u(x)→+∞ as dist (x,∂Ω)→0 . Our analysis is based on the Karamata regular variation theory. To cite this article: F.-C. Cirstea, V. Rădulescu, C. R. Acad. Sci. Paris, Ser. I 336 (2003).