2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61262In this paper we perform a fine blow-up analysis for a fourth order elliptic equation involving critical Sobolev exponent, related to the prescription of some conformal invariant on the standard sphere. We derive from this analysis some a priori estimates in dimension 5 and 6. On the five dimensionl sphere these a priori estimates combined with the perturbation result of Part I allow us to obtain some existence results. On the six dimensional sphere we prove the existence of at least one solution when an associated index is different from zero.Analysis of PDEsDifferential Geometry53C21; 35B45; 35J60; 53A30; 58G30text