{
  "id": "1701.02376",
  "version": "v1",
  "published": "2017-01-09T22:23:20.000Z",
  "updated": "2017-01-09T22:23:20.000Z",
  "title": "Ground state solutions for a nonlinear Choquard equation",
  "authors": [
    "Luca Battaglia"
  ],
  "comment": "8 pages, survey of my talk at the Bru-To PDE's conference",
  "categories": [
    "math.AP"
  ],
  "abstract": "We discuss the existence of ground state solutions for the Choquard equation $$-\\Delta u=(I_\\alpha*F(u))F'(u)\\quad\\quad\\quad\\text{in }\\mathbb R^N.$$ We prove the existence of solutions under general hypotheses, investigating in particular the case of a homogeneous nonlinearity $F(u)=\\frac{|u|^p}p$. The cases $N=2$ and $N\\ge3$ are treated differently in some steps. The solutions are found through a variational mountain pass strategy. The result presented are contained in the papers with arXiv ID 1212.2027 and 1604.03294",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-09T22:23:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J91",
      "35J20"
    ],
    "keywords": [
      "ground state solutions",
      "nonlinear choquard equation",
      "variational mountain pass strategy",
      "general hypotheses",
      "nonlinearity"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}