Existence of conformal metrics with prescribed Q-curvature (Q370043)

Summary: We consider the problem of existence of conformal metrics with prescribed Q-curvature on the standard sphere \(S^n\), \(n \geq 5\). Under the assumption that the order of flatness at critical points of the prescribed Q-curvature function \(K(x)\) is \(\beta \in ]1, n - 4]\), we give precise estimates on the losses of compactness, and we prove new existence and multiplicity results through an Euler-Hopf type formula.