Abstract
We prove compactness and existence results for a scalar curvature-type equation on a bounded domain of
. The problem has a variational structure with lack of compactness. Using an asymptotic analysis and dynamical arguments, we characterize the accumulation points of all non-compact flow-lines of the gradient vector field, the so-called critical points at infinity. We then associate to each critical point at infinity a Morse index, which enables us to derive a Bahri-Coron index type criteria and to establish the existence.