{
  "id": "1506.00056",
  "version": "v1",
  "published": "2015-05-30T01:27:36.000Z",
  "updated": "2015-05-30T01:27:36.000Z",
  "title": "Compactness and existence results in weighted Sobolev spaces of radial functions. Part II: Existence",
  "authors": [
    "Marino Badiale",
    "Michela Guida",
    "Sergio Rolando"
  ],
  "comment": "29 pages, 8 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove existence and multiplicity results for finite energy solutions to the nonlinear elliptic equation \\[ -\\triangle u+V\\left( \\left| x\\right| \\right) u=g\\left( \\left| x\\right| ,u\\right) \\quad \\textrm{in }\\Omega \\subseteq \\mathbb{R}^{N},\\ N\\geq 3, \\] where $\\Omega $ is a radial domain (bounded or unbounded) and $u$ satisfies $u=0$ on $\\partial \\Omega $ if $\\Omega \\neq \\mathbb{R}^{N}$ and $u\\rightarrow 0$ as $\\left| x\\right| \\rightarrow \\infty $ if $\\Omega $ is unbounded. The potential $V$ may be vanishing or unbounded at zero or at infinity and the nonlinearity $g$ may be superlinear or sublinear. If $g$ is sublinear, the case with $g\\left( \\left| \\cdot \\right| ,0\\right) \\neq 0$ is also considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-30T01:27:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35J20",
      "35Q55",
      "35J25"
    ],
    "keywords": [
      "weighted sobolev spaces",
      "radial functions",
      "existence results",
      "compactness",
      "finite energy solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150600056B"
    }
  }
}