Boundary behaviour for solutions of boundary blow-up problems in a borderline case

We investigate boundary blow-up solutions of the equation Δ u = f ( u ) in a bounded domain Ω ⊂ R N under the condition that f ( t ) has a relatively slow growth as t goes to infinity. We show how the mean curvature of the boundary ∂Ω appears in the asymptotic expansion of the solution u ( x ) in terms of the distance of x from ∂Ω.