{
  "id": "1905.11120",
  "version": "v1",
  "published": "2019-05-27T11:05:59.000Z",
  "updated": "2019-05-27T11:05:59.000Z",
  "title": "On the Schrödinger-Poisson system with indefinite potential and $3$-sublinear nonlinearity",
  "authors": [
    "Sunra J. N. Mosconi",
    "Shibo Liu"
  ],
  "comment": "23 pages, comments welcome!",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a class of stationary Schr\\\"{o}dinger-Poisson systems with a general nonlinearity $f(u)$ and coercive sign-changing potential $V$ so that the Schr\\\"{o}dinger operator $-\\Delta+V$ is indefinite. Previous results in this framework required $f$ to be strictly $3$-superlinear, thus missing the paramount case of the Gross-Pitaevskii-Poisson system, where $f(t)=|t|^{2}t$; in this paper we fill this gap, obtaining non-trivial solutions when $f$ is not necessarily $3$-superlinear.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-27T11:05:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "58E05"
    ],
    "keywords": [
      "indefinite potential",
      "sublinear nonlinearity",
      "schrödinger-poisson system",
      "general nonlinearity",
      "superlinear"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}