Abstract

We construct solutions of the Liouville equation. δu+ε2eu=0in Ω with Ω a smooth bounded domain in R2, with Robin boundary condition. ∂u∂ν+λu=0on ∂Ω. The solutions constructed exhibit concentration as ε → 0 and simultaneously as 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. © 2011 Elsevier Inc.