We give a series of very general sufficient conditions in order to ensure the uniqueness of large solutions for −∆u + f (x, u) = 0 in a bounded domain Ω where f : Ω × R → R + is a continuous function, such that f (x, 0) = 0 for x ∈ Ω, and f (x, r) > 0 for x in a neighborhood of ∂Ω and all r > 0. 2010 Mathematics Subject Classification. 35 J 61; 31 B 15; 28 C 05 .