{
  "id": "2203.06702",
  "version": "v1",
  "published": "2022-03-13T16:34:12.000Z",
  "updated": "2022-03-13T16:34:12.000Z",
  "title": "Existence, structure, and robustness of ground states of a NLSE in 3D with a point defect",
  "authors": [
    "Riccardo Adami",
    "Filippo Boni",
    "Raffaele Carlone",
    "Lorenzo Tentarelli"
  ],
  "comment": "18 pages. Contribution for the special issue of the \"XX International Congress on Mathematical Physics\". Keywords:standing waves, nonlinear Schr\\\"odinger, ground states, delta interaction, radially symmetric solutions, rearrangements",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the ground states for the Schr\\\"odinger equation with a focusing nonlinearity and a point interaction in dimension three. We establish that ground states exist for every value of the mass; moreover they are positive, radially symmetric, decreasing along the radial direction, and show a Coulombian singularity at the location of the point interaction. Remarkably, the existence of the ground states is independent of the attractive or repulsive character of the point interaction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-13T16:34:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q40",
      "35Q55",
      "35B07",
      "35B09",
      "35R99",
      "49J40",
      "49N15"
    ],
    "keywords": [
      "ground states",
      "point defect",
      "point interaction",
      "robustness",
      "radial direction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}