A Bahri-Brezis type problem on asymptotically hyperbolic manifolds

Abstract

In this paper, we study a Bahri-Brezis type problem on a compact 3-dimensional asymptotically hyperbolic manifold. Using the celebrated Algebraic Topological argument of Bahri-Coron, we show the existence of at least one solution under the assumption that the corresponding degenerate boundary value problem has a positive first eigenvalue and a positive Green function.