{
  "id": "0709.2878",
  "version": "v1",
  "published": "2007-09-18T16:46:21.000Z",
  "updated": "2007-09-18T16:46:21.000Z",
  "title": "Singular limits for the bi-laplacian operator with exponential nonlinearity in $\\R^4$",
  "authors": [
    "Mónica Clapp",
    "Claudio Muñoz",
    "Monica Musso"
  ],
  "comment": "30 pages, to appear in Ann. IHP Non Linear Analysis",
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $\\Omega$ be a bounded smooth domain in $\\mathbb{R}^{4}$ such that for some integer $d\\geq1$ its $d$-th singular cohomology group with coefficients in some field is not zero, then problem {\\Delta^{2}u-\\rho^{4}k(x)e^{u}=0 & \\hbox{in}\\Omega, u=\\Delta u=0 & \\hbox{on}\\partial\\Omega, has a solution blowing-up, as $\\rho\\to0$, at $m$ points of $\\Omega$, for any given number $m$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-09-18T16:46:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exponential nonlinearity",
      "singular limits",
      "bi-laplacian operator",
      "th singular cohomology group",
      "solution blowing-up"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008AnIHP..25.1015C"
    }
  }
}