Infinitely many solutions for the prescribed scalar curvature problem on SNSN

We consider the following prescribed scalar curvature problem on SNSNequation(∗){−ΔSNu+N(N−2)2u=K˜uN+2N−2onSN,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.