Abstract
There have been many works on the problem of finding a conformal metric on the standard sphere S-n, n >= 3, when the prescribed scalar curvature function is flat near its critical points with order of flatness beta. All the existence results up to this research concern the case 1 < beta < n. The present paper deals with the case beta >= n. We provide a complete analysis of the asymptotic expansion of the associated gradient vector field for any beta > 1. Moreover, we establish (in this first part) existence results concerning some cases of beta >= n. (C) 2016 Elsevier B.V. All rights reserved.