On the prescribed fractional Q-curvatures problem on Sn under pinching conditions

Abstract

In this paper, we study the prescribed fractional Q-curvatures problem of order 2σ on the n-dimensional standard sphere $(S^n,g_0)$, where $n\ge 3$, $\sigma \in (0,\frac{n-2}{2})$. By combining critical points at infinity approach with Morse theory we obtain new existence results under suitable pinching conditions.