Doubling the equatorial for the prescribed scalar curvature problem on

Abstract

We consider the prescribed scalar curvature problem on SNΔSNv−N(N−2)2v+K~(y)vN+2N−2=0 on SN,v>0in SN, 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.