{
  "id": "2212.07561",
  "version": "v1",
  "published": "2022-12-15T00:29:39.000Z",
  "updated": "2022-12-15T00:29:39.000Z",
  "title": "Monotonicity of the period map for the equation $-\\varphi''+\\varphi-\\varphi^{k}=0$",
  "authors": [
    "Fábio Natali",
    "Giovana Alves"
  ],
  "comment": "9 pages",
  "categories": [
    "math.DS",
    "math.CA"
  ],
  "abstract": "In this paper, we establish the monotonicity of the period map in terms of the energy levels for some periodic solutions of the equation $-\\varphi''+\\varphi-\\varphi^{k}=0$, where $k>1$ is a real number. We present a different approach to show this property by using the spectral information of the corresponding linearized operator around the periodic solution and tools about the Floquet theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-15T00:29:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B10",
      "35J61",
      "47A75"
    ],
    "keywords": [
      "period map",
      "monotonicity",
      "periodic solution",
      "floquet theory",
      "energy levels"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}