{
  "id": "1708.01331",
  "version": "v1",
  "published": "2017-08-03T23:54:04.000Z",
  "updated": "2017-08-03T23:54:04.000Z",
  "title": "Multispike solutions for the Brezis-Nirenberg problem in dimension three",
  "authors": [
    "M. Musso",
    "D. Salazar"
  ],
  "comment": "38 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the problem $\\Delta u + \\lambda u +u^5 = 0$, $u>0$, in a smooth bounded domain $\\Omega$ in ${\\mathbb R}^3$, under zero Dirichlet boundary conditions. We obtain solutions to this problem exhibiting multiple bubbling behavior at $k$ different points of the domain as $\\lambda$ tends to a special positive value $\\lambda_0$, which we characterize in terms of the Green function of $-\\Delta - \\lambda$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-03T23:54:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J25",
      "35J66"
    ],
    "keywords": [
      "brezis-nirenberg problem",
      "multispike solutions",
      "zero dirichlet boundary conditions",
      "problem exhibiting multiple bubbling behavior",
      "special positive value"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}