{
  "id": "1812.03642",
  "version": "v1",
  "published": "2018-12-10T06:34:31.000Z",
  "updated": "2018-12-10T06:34:31.000Z",
  "title": "Solutions of the Yamabe Equation By Lyapunov-Schmidt Reduction",
  "authors": [
    "Jorge Davila",
    "Isidro H. Munive"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Given any closed Riemannian manifold $(M,g)$ we use the Lyapunov-Schmidt finite-dimensional reduction method to prove multiplicity results for positive solutions of a subcritical Yamabe type equation on $(M,g)$. If $(N,h)$ is a closed Riemannian manifold of constant positive scalar curvature our result gives multiplicity results for the Yamabe equation on the Riemannian product $(M\\times N, g + \\epsilon^{2} h)$, for $\\epsilon >0$ small.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-10T06:34:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "yamabe equation",
      "lyapunov-schmidt reduction",
      "closed riemannian manifold",
      "multiplicity results",
      "lyapunov-schmidt finite-dimensional reduction method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}