{
  "id": "1511.02165",
  "version": "v1",
  "published": "2015-11-05T08:27:38.000Z",
  "updated": "2015-11-05T08:27:38.000Z",
  "title": "Semilinear equations associated with Dunkl Laplacian",
  "authors": [
    "Mohamed Ben Chrouda",
    "Khalifa El Mabrouk",
    "Kods Hassine"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $\\Delta_k$ be the Dunkl Laplacian on $\\mathbb R^d$ associated with a reflection group $W$ and a multiplicity function $k$. The purpose of this paper is to establish necessary and sufficient condition under which there exists a positive solution of the equation $\\Delta_ku=\\varphi(u)$ in the unit ball of $\\mathbb R^d$ as well as in the whole space $\\mathbb R^d$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-05T08:27:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31B05",
      "31B15",
      "35J08",
      "35J61"
    ],
    "keywords": [
      "dunkl laplacian",
      "semilinear equations",
      "reflection group",
      "multiplicity function",
      "sufficient condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151102165B"
    }
  }
}