Uniqueness of the blow-up boundary solution of logistic equations with absorbtion

Abstract Let Ω be a smooth bounded domain in R N . Assume f∈C1[0,∞) is a non-negative function 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 . We study the logistic equation Δu+au=b(x)f(u) in Ω . The special feature of this work is the uniqueness of positive solutions blowing-up on ∂Ω , in a general setting that arises in probability theory. To cite this article: F.-C. Cirstea, V. Rădulescu, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 447–452.