{
  "id": "1612.07914",
  "version": "v1",
  "published": "2016-12-23T09:40:35.000Z",
  "updated": "2016-12-23T09:40:35.000Z",
  "title": "Ground states for fractional Kirchhoff equations with critical nonlinearity in low dimension",
  "authors": [
    "Zhisu Liu",
    "Marco Squassina",
    "Jianjun Zhang"
  ],
  "comment": "25 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the existence of ground states to a nonlinear fractional Kirchhoff equation with an external potential $V$. Under suitable assumptions on $V$, using the monotonicity trick and the profile decomposition, we prove the existence of ground states. In particular, the nonlinearity does not satisfy the Ambrosetti-Rabinowitz type condition or monotonicity assumptions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-23T09:40:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35Q51",
      "53C35"
    ],
    "keywords": [
      "ground states",
      "low dimension",
      "critical nonlinearity",
      "nonlinear fractional kirchhoff equation",
      "ambrosetti-rabinowitz type condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}