Regular solutions to a supercritical elliptic problem in exterior domains

Abstract

We consider the supercritical elliptic problem -Δu = λe^u, λ> 0, in an exterior domain $\Omega ={\mathbb{R}}^N\setminus D$ under zero Dirichlet condition, where D is smooth and bounded in \mathbb{R}^N, N greater or equal than 3. We prove that, for λsmall, this problem admits infinitely many regular solutions.