{
  "id": "1506.07317",
  "version": "v1",
  "published": "2015-06-24T11:05:20.000Z",
  "updated": "2015-06-24T11:05:20.000Z",
  "title": "Qualitative properties of positive solutions to nonlocal critical problems involving the Hardy-Leray potential",
  "authors": [
    "Serena Dipierro",
    "Luigi Montoro",
    "Ireneo Peral",
    "Berardino Sciunzi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove the existence, qualitative properties and asymptotic behavior of positive solutions to the doubly critical problem $$ (-\\Delta)^s u=\\vartheta\\frac{u}{|x|^{2s}}+u^{2_s^*-1}, \\quad u\\in \\dot{H}^s(\\mathbb{R}^N).$$ The technique that we use to prove the existence is based on variational arguments. The qualitative properties are obtained by using of the moving plane method, in a nonlocal setting, on the whole $\\mathbb{R}^N$ and by some comparison results. Moreover, in order to find the asymptotic behavior of solutions, we use a representation result that allows to transform the original problem into a different nonlocal problem in a weighted fractional space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-24T11:05:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "qualitative properties",
      "nonlocal critical problems",
      "positive solutions",
      "hardy-leray potential",
      "asymptotic behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150607317D"
    }
  }
}