We　use　blow　up　analysis　for　local　integral　equations　to　prove　compactness　of　solutions　to　higher-order　critical　elliptic　equations　provided　the　potentials　only　have　non-degenerate　zeros.　Secondly,　corresponding　to　Schoen＇s　Weyl　tensor　vanishing　conjecture　for　the　Yamabe　equation　on　manifolds,　we　establish　a　Laplacian　vanishing　rate　of　the　potentials　at　blow　up　points　of　solutions.