{
  "id": "1604.03294",
  "version": "v1",
  "published": "2016-04-12T08:26:34.000Z",
  "updated": "2016-04-12T08:26:34.000Z",
  "title": "Existence of groundstates for a class of nonlinear Choquard equations in the plane",
  "authors": [
    "Luca Battaglia",
    "Jean Van Schaftingen"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove the existence of a nontrivial groundstate solution for the class of nonlinear Choquard equation $$ -\\Delta u+u=(I_\\alpha*F(u))F'(u)\\qquad\\text{in }\\mathbb{R}^2, $$ where $I_\\alpha$ is the Riesz potential of order $\\alpha$ on the plane $\\mathbb{R}^2$ under general nontriviality, growth and subcriticality on the nonlinearity $F \\in C (\\mathbb{R},\\mathbb{R})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-12T08:26:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J91",
      "35J20"
    ],
    "keywords": [
      "nonlinear choquard equation",
      "nontrivial groundstate solution",
      "riesz potential",
      "general nontriviality",
      "nonlinearity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160403294B"
    }
  }
}