  In this paper, using the theory of critical points at infinity of Bahri, we
derive an exact bubbling rate formula for the resonant prescribed Q-curvature
equation on closed even-dimensional Riemannian manifolds. Using this, we derive
new existence results for the resonant prescribed Q-curvature problem under a
positive mass type assumption. Moreover, we derive a compactness theorem for
conformal metrics with prescribed Q-curvature under a non-degeneracy
assumption. Furthermore, combining the bubbling rate formula with the
construction of some blowing-up solutions, we compute the Leray-Schauder degree
of the resonant prescribed Q-curvature equation under a non-degeneracy and
Morse type assumption.
