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

TL;DR

This paper establishes new existence results for the prescribed fractional Q-curvature problem on spheres using advanced mathematical techniques, under specific geometric conditions.

Contribution

It introduces novel existence results for fractional Q-curvature problems on spheres by applying critical points at infinity and Morse theory under pinching conditions.

Findings

Existence of solutions under certain pinching conditions.

Application of critical points at infinity method.

Use of Morse theory to analyze solution existence.

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 $n\geq3$, $\sigma\in(0,\frac{n-2}{2})$. By combining critical points at infinity approach with Morse theory we obtain new existence results under suitable pinching conditions.