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

摘要

We consider the prescribed scalar curvature problem on SN. SN v - N(N - 2) 2 v + K (y)v N+2 N-2 = 0 on SN, v> 0 inSN, 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.