Conformal metrics on $R^{2m}$ with constant Q-curvature, prescribed volume and asymptotic behavior

Ali Hyder, Luca Martinazzi

We study the solutions $u\in C^{\infty }(R^{2m})$ of the problem $(-\Delta {)}^{m}u=Q{e}^{2mu}$, where $Q=\pm (2m-1)!$, and $V:={\int }_{R^{2m}}{e}^{2mu}dx<\infty$, particularly when $m>1$. This c…