2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67462In this paper we study the problem of prescribing a fourth order conformal invariant (the Paneitz curvature) on the $n$-sphere, with $n\geq 5$. Using tools from the theory of critical points at infinity, we provide some topological conditions on the level sets of a given positive function under which we prove the existene of a metric, conformally equivalent to the standard metric, with prescribed Paneitz curvature.20 pagesAnalysis of PDEs35J60; 53C21; 58J05text