### Existence of conformal metrics on $S^n$ with prescribed fourth-order invariant

Veronica Felli

#### Abstract

In this paper we prescribe a fourth-order conformal invariant on the standard $n$-sphere, with $n\geq5$, and study the related fourth-order elliptic equation. We first find some existence results in the perturbative case. After some blow-up analysis we build a homotopy to pass from the perturbative case to the nonperturbative one under some flatness condition. Finally we state some existence results under the assumption of symmetry.

#### Article information

Source
Adv. Differential Equations, Volume 7, Number 1 (2002), 47-76.

Dates
First available in Project Euclid: 27 December 2012

Felli, Veronica. Existence of conformal metrics on $S^n$ with prescribed fourth-order invariant. Adv. Differential Equations 7 (2002), no. 1, 47--76. https://projecteuclid.org/euclid.ade/1356651875