{
  "id": "1703.04353",
  "version": "v1",
  "published": "2017-03-13T12:15:26.000Z",
  "updated": "2017-03-13T12:15:26.000Z",
  "title": "Nonexistence of positive solutions for Henon equation",
  "authors": [
    "Jorge Garcia-Melian"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the semilinear elliptic equation $$ -\\Delta u = |x|^\\alpha u^p \\quad \\hbox{in } \\mathbb{R}^N, $$ where $N\\ge 3$, $\\alpha>-2$ and $p>1$. We show that there are no positive solutions provided that the exponent $p$ additionally verifies $$ 1<p<\\frac{N+2\\alpha+2}{N-2}. $$ This solves an open problem posed in previous literature, where only the radially symmetric case was fully understood. We also characterize all positive solutions when $p=\\frac{N+2\\alpha+2}{N-2}$ and $-2<\\alpha<0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-13T12:15:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive solutions",
      "henon equation",
      "nonexistence",
      "semilinear elliptic equation",
      "open problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}