Asymptotic behaviour of large solutions of an elliptic quasilinear equation in a borderline case

Given a bounded smooth domain Omega in R-N, We study the asymptotic behavio ur close to the boundary partial derivative Omega of the large solutions of the equation Deltau - /Du/(q) = f(u), where 1 < q < 2 and f(u)u(q/(q-2)) c onverges to a positive number, as u tends to infinity. Existence and asymptotic behaviour of large solutions of this equation are studied also in [2] for a general f(u). However, the assumptions considered in [2] do not apply to the case studied in this Note. As a consequence of the asymptotic behaviour we also show an uniqueness res ult. (C) 2000 Academie des sciences/Editions scientifiques et medicales Els evier SAS.