Doubling the equatorial for the prescribed scalar curvatureproblem on ${\mathbb{S}}^N$

Note: Please see pdf for full abstract with equations. We consider the prescribed scalar curvature problem on S N Δ SN v −N(N − 2)/2 v + ​​ K̃ (y)v N+2/N−2 = 0 on S N , v > 0 in S N , under the assumptions that the scalar curvature ​ K̃ 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.