Uniqueness of positive solutions for a boundary blow-up problem

In this paper we prove the uniqueness of the positive solution for the boundary blow-up problem { Δ u = f ( u ) in Ω , u = ∞ on ∂ Ω , where Ω is a C 2 bounded domain in R N , under the hypotheses that f ( t ) is nondecreasing in t > 0 and f ( t ) / t p is increasing for large t and some p > 1 . We also consider the uniqueness of a related problem when the equation includes a nonnegative weight a ( x ) .