{
  "id": "1201.3736",
  "version": "v1",
  "published": "2012-01-18T09:51:43.000Z",
  "updated": "2012-01-18T09:51:43.000Z",
  "title": "The Brezis--Nirenberg problem for the Hénon equation: ground state solutions",
  "authors": [
    "Simone Secchi"
  ],
  "comment": "To appear on Advanced Nonlinear Studies",
  "categories": [
    "math.AP"
  ],
  "abstract": "This work is devoted to the Dirichlet problem for the equation (-\\Delta u = \\lambda u + |x|^\\alpha |u|^{2^*-2} u) in the unit ball of $\\mathbb{R}^N$. We assume that $\\lambda$ is bigger than the first eigenvalues of the laplacian, and we prove that there exists a solution provided $\\alpha$ is small enough. This solution has a variational characterization as a ground state.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-01-18T09:51:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "35J61",
      "35J91"
    ],
    "keywords": [
      "ground state solutions",
      "hénon equation",
      "brezis-nirenberg problem",
      "unit ball",
      "first eigenvalues"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.3736S"
    }
  }
}