{
  "id": "1803.09246",
  "version": "v2",
  "published": "2018-03-25T12:58:24.000Z",
  "updated": "2018-11-19T12:39:16.000Z",
  "title": "Ground states of the $L^2$-critical NLS equation with localized nonlinearity on a tadpole graph",
  "authors": [
    "Simone Dovetta",
    "Lorenzo Tentarelli"
  ],
  "comment": "12 pages, 5 figures. Keywords: minimization, metric graphs, critical growth, nonlinear Schr\\\"odinger equation, localized nonlinearity",
  "journal": "Oper. Theory Adv. Appl. 281 (2020), 113-125",
  "doi": "10.1007/978-3-030-44097-8_5",
  "categories": [
    "math.AP"
  ],
  "abstract": "The paper aims at giving a first insight on the existence/nonexistence of ground states for the $L^2$-critical NLS equation on metric graphs with localized nonlinearity. In particular, we focus on the tadpole graph, which, albeit being a toy model, allows to point out some specific features of the problem, whose understanding will be useful for future investigations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2018-11-19T12:39:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R02",
      "35Q55",
      "81Q35",
      "49J40"
    ],
    "keywords": [
      "critical nls equation",
      "ground states",
      "tadpole graph",
      "localized nonlinearity",
      "paper aims"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}