{
  "id": "1203.3154",
  "version": "v1",
  "published": "2012-03-14T17:44:36.000Z",
  "updated": "2012-03-14T17:44:36.000Z",
  "title": "Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains",
  "authors": [
    "Vitaly Moroz",
    "Jean Van Schaftingen"
  ],
  "comment": "47 pages, 8 figures",
  "journal": "J. Differential Equations 254 (2013), no. 8, 3089-3145",
  "doi": "10.1016/j.jde.2012.12.019",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a semilinear elliptic problem with a nonlinear term which is the product of a power and the Riesz potential of a power. This family of equations includes the Choquard or nonlinear Schroedinger--Newton equation. We show that for some values of the parameters the equation does not have nontrivial nonnegative supersolutions in exterior domains. The same techniques yield optimal decay rates when supersolutions exists.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-03-14T17:44:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J61",
      "35B09",
      "35B33",
      "35B40",
      "35J45",
      "35Q55",
      "45K05"
    ],
    "keywords": [
      "exterior domains",
      "choquard equations",
      "supersolutions",
      "techniques yield optimal decay rates",
      "nonexistence"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Differential Equations",
      "year": 2013,
      "volume": 254,
      "number": 8,
      "pages": 3089
    },
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013JDE...254.3089M"
    }
  }
}