{
  "id": "1308.3115",
  "version": "v2",
  "published": "2013-08-14T13:23:33.000Z",
  "updated": "2013-08-15T04:42:47.000Z",
  "title": "Positive radial solutions for coupled Schrödinger system with critical exponent in $\\R^N\\,(N\\geq5)$",
  "authors": [
    "Yan-fang Peng",
    "Hong-yu Ye"
  ],
  "comment": "22 pages. arXiv admin note: text overlap with arXiv:1209.2522 by other authors. text overlap with arXiv:1209.2522 by other authors",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the following coupled Schr\\\"odinger system \\ds -\\Delta u+u=u^{2^*-1}+\\be u^{\\frac{2^*}{2}-1}v^{\\frac{2^*}{2}}+\\la_1u^{\\al-1}, &x\\in \\R^N, \\ds -\\Delta v+v=v^{2^*-1}+\\be u^{\\frac{2^*}{2}}v^{\\frac{2^*}{2}-1}+\\la_2v^{r-1}, &x\\in \\R^N, u,v > 0, &x\\in \\R^N, where $N\\geq 5, \\la_1,\\la_2>0,\\be\\neq 0, 2<\\al,r<2^*,2^*\\triangleq \\frac{2N}{N-2}.$ Note that the nonlinearity and the coupling terms are both critical. Using the Mountain Pass Theorem, Ekeland's variational principle and Nehari mainfold, we show that this critical system has a positive radial solution for positive $\\be$ and some negative $\\be$ respectively.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-08-15T04:42:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive radial solution",
      "coupled schrödinger system",
      "critical exponent",
      "ekelands variational principle",
      "mountain pass theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.3115P"
    }
  }
}