Obstructions to prescribed Q-curvature of complete conformal metrics on ${\mathbb{R}}^n$

We provide some obstructions to the prescribed Q-curvature problem for the complete conformal metrics on ${\mathbb{R}}^n$ with finite total Q-curvature. One of them is a Bonnet-Mayer type theorem with respect to Q-curvature. Others are related to the decay rate of the prescribed functions.