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

Given a smooth function $f(x)$ on ${\mathbb{R}}^n$ which is positive somewhere and satisfies $f(x)=O(\mathrm{\mid }x{\mathrm{\mid }}^{-l})$ for any $l>\frac{n}{2}$, we show that there exists a complete and conformal metric $g=e^{2u}\mathrm{\mid }dx{\mathrm{\mid }}^2$ with finite total Q-curvature such that its Q-curvature equals to $f(x)$.