Singular limit of radial solutions in an annulus

In this paper we study the radial solutions of the problem

$\[\cases{-\Delta u=\lambda\mathrm{e}^{u}& \mbox{in} \varOmega,\cr u=0& \mbox{on} \partial\varOmega,}\]$

where Ω is an annulus of R^N, N≥2 and λ is close to zero.

Among the other results we show the existence of a singular limit and some qualitative properties of the solution.