{
  "id": "1403.3211",
  "version": "v3",
  "published": "2014-03-13T09:34:34.000Z",
  "updated": "2014-07-21T08:01:09.000Z",
  "title": "Positive ground states for a system of Schrödinger equations with critically growing nonlinearities",
  "authors": [
    "Pietro d'Avenia",
    "Jarosław Mederski"
  ],
  "comment": "19 pages, pre-peer version, to appear in Calc. Var. Partial Differential Equations",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the following problem \\[ \\begin{cases} -\\Delta u = \\lambda u + u^{2^*-2} v & \\hbox{in} \\Omega,\\\\ -\\Delta v= \\mu v^{2^*-1} + u^{2^*-1} & \\hbox{in} \\Omega,\\\\ u> 0,v> 0 & \\hbox{in} \\Omega,\\\\ u=v=0 & \\hbox{on} \\partial \\Omega, \\end{cases} \\] where $\\Omega$ is a bounded domain of $\\mathbb{R}^N$, $N\\geq 4$, $2^*=2N/(N-2)$, $\\lambda\\in\\mathbb{R}$ and $\\mu\\geq 0$ and we obtain existence and nonexistence results, depending on the value of the parameters $\\lambda$ and $\\mu$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-07-21T08:01:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J57",
      "35A01",
      "35B33",
      "35J50"
    ],
    "keywords": [
      "positive ground states",
      "critically growing nonlinearities",
      "schrödinger equations",
      "nonexistence results",
      "bounded domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.3211D"
    }
  }
}