Non-compactness and Multiplicity Results for the Yamabe Problem on Sn

The aim of this paper is to show the existence of metrics gε on Sn, where gε is a perturbation of the standard metric g0, for which the Yamabe problem possesses a sequence of solutions unbounded in L∞(Sn). The metrics gε that we find are of class Ck on Sn with (k⩽n−34). We also prove some new multiplicity results.