2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147629Necessary and sufficient conditions are given for the Palais-Smale Condition C to hold for the Yang-Mills functional for invariant connections on a principal bundle over a compact manifold of any dimension. It is assumed that the connections are invariant under the action of a compact Lie group on the manifold, and that all orbits of the action have codimension three or less.25 pages, plain TeX. Revised version: the paper has been reorganized, some minor errors have been corrected, more examples have been addedDifferential Geometry58E15 (Primary) 53C07, 58E40, 81T13 (Secondary)text