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.
Citation
Veronica Felli. "Existence of conformal metrics on $S^n$ with prescribed fourth-order invariant." Adv. Differential Equations 7 (1) 47 - 76, 2002. https://doi.org/10.57262/ade/1356651875
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