{
  "id": "1811.02387",
  "version": "v1",
  "published": "2018-11-06T14:57:56.000Z",
  "updated": "2018-11-06T14:57:56.000Z",
  "title": "$L^2$-critical NLS on noncompact metric graphs with localized nonlinearity: topological and metric features",
  "authors": [
    "Simone Dovetta",
    "Lorenzo Tentarelli"
  ],
  "comment": "22 pages, 7 figures. Keywords: metric graphs, NLS, ground states, localized nonlinearity, $L^2$-critical case",
  "categories": [
    "math.AP",
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "Carrying on the discussion initiated in (Dovetta-Tentarelli'18), we investigate the existence of ground states of prescribed mass for the $L^2$-critical NonLinear Schr\\\"odinger Equation (NLSE) on noncompact metric graphs with localized nonlinearity. Precisely, we show that the existence (or nonexistence) of ground states mainly depends on a parameter called reduced critical mass, and then we discuss how the topological and metric features of the graphs affect such a parameter, establishing some relevant differences with respect to the case of the extended nonlinearity studied by (Adami-Serra-Tilli'17). Our results rely on a thorough analysis of the optimal constant of a suitable variant of the $L^2$-critical Gagliardo-Nirenberg inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-06T14:57:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R02",
      "35Q55",
      "81Q35",
      "35Q40",
      "49J40"
    ],
    "keywords": [
      "noncompact metric graphs",
      "metric features",
      "localized nonlinearity",
      "critical nls",
      "ground states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}