Doubling the equatorial for the prescribed scalar curvature problem on S^N

We consider the prescribed scalar curvature problem on S^NΔSNv-N(N-2)2v+K~(y)vN+2N-2=0onSN,v>0inSN,under the assumptions that the scalar curvature K~ is rotationally symmetric, and has a positive local maximum point between the poles. We prove the existence of infinitely many non-radial positive solutions, whose energy can be made arbitrarily large. These solutions are invariant under some non-trivial sub-group of O(3) obtained doubling the equatorial. We use the finite dimensional Lyapunov–Schmidt reduction method.