Non-compactness and multiplicity results for the Yamabe problem on S(n)

The aim of this paper is to show the existence of metrics (g) over bar (epsilon) on S(n), where (g) over bar (epsilon) is a perturbation of the standard metric (g) over bar (o), for which the Yamabe problem possesses a sequence of solutions unbounded in L(infinity)(S(n)). The metrics (g) over bar (epsilon) that we iind are of class C(k) On S(n) With (k less than or equal ton-3/4). We also prove some new multiplicity results.