Regular solutions to a super critical elliptic problem in exterior domains

Abstract

We consider the supercritical elliptic problem −Δu=λeu, λ>0, in an exterior domain Ω=RN∖D under zero Dirichlet condition, where D is smooth and bounded in RN, N⩾3. We prove that, for λ small, this problem admits infinitely many regular solutions.zero Dirichlet condition, where D is smoot hand bounded in RN, N 3. We prove that,for λ small, this problem admits infinitely many regular solutions.