Infinitely many solutions for the prescribed scalar curvature problem on SN

We consider the following prescribed scalar curvature problem on S-N {-Delta(SN)u + N(N - 2)/2 u = (K) over tildeu(N+2/N-2) on S-N (*) u > 0 where (K) over tilde is positive and rotationally symmetric. We show that if (K) over tilde has a local maximum point between the poles then Eq. (*) has infinitely many non-radial positive solutions, whose energy can be made arbitrarily large.(C) 2009 Elsevier Inc. All rights reserved.