{
  "id": "1709.09867",
  "version": "v1",
  "published": "2017-09-28T09:30:31.000Z",
  "updated": "2017-09-28T09:30:31.000Z",
  "title": "The $1$-Yamabe equation on graph",
  "authors": [
    "Huabin Ge",
    "Wenfeng Jiang"
  ],
  "comment": "10 pages. All comments are welcome",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We study the following $1$-Yamabe equation on a connected finite graph $$\\Delta_1u+g\\mathrm{Sgn}(u)=h|u|^{\\alpha-1}\\mathrm{Sgn}(u),$$ where $\\Delta_1$ is the discrete $1$-Laplacian, $\\alpha>1$ and $g, h>0$ are known. We show that the above $1$-Yamabe equation always has a nontrivial solution $u\\geq0$, $u\\neq0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-28T09:30:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "yamabe equation",
      "connected finite graph",
      "nontrivial solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}