2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61223In 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 non-perturbative one under some flatness condition. Finally we state some existence results under the assumption of symmetry.30 pagesAnalysis of PDEsDifferential Geometrytext