Concentrating solutions of the Liouville equation with Robin boundary condition

We construct solutions of the Liouville equationΔu+ϵ2eu=0in Ω with Ω   a smooth bounded domain in R2R2, with Robin boundary condition∂u∂ν+λu=0on ∂Ω. The solutions constructed exhibit concentration as ϵ→0ϵ→0 and simultaneously as λ→+∞λ→+∞, at points that get close to the boundary, and shows that in general the set of solutions of this problems exhibits a richer structure than the problem with Dirichlet boundary conditions.