New existence results for prescribed fractional $Q$-curvatures problem on ${\mathbb{S}}^n$ under pinching conditions

Abstract

In this paper we study the prescribed fractional $Q$-curvatures problem of order $2\sigma$ on the $n$-dimensional standard sphere $({\mathbb{S}}^n,g_0)$, 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.

arXiv admin note: substantial text overlap with arXiv:2109.05981, arXiv:2012.12973 by other authors