Infinitely many solutions for the prescribed scalar curvature problem on SN

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