{
  "id": "1912.11231",
  "version": "v1",
  "published": "2019-12-24T07:07:23.000Z",
  "updated": "2019-12-24T07:07:23.000Z",
  "title": "A limit equation and bifurcation diagrams of semilinear elliptic equations with general supercritical growth",
  "authors": [
    "Yasuhito Miyamoto"
  ],
  "comment": "21 pages",
  "journal": "J. Differential Equations 264 (2018), 2684--2707",
  "doi": "10.1016/j.jde.2017.10.034",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study radial solutions of the semilinear elliptic equation $\\Delta u+f(u)=0$ under rather general growth conditions on $f$. We construct a radial singular solution and study the intersection number between the singular solution and a regular solution. An application to bifurcation problems of elliptic Dirichlet problems is given. To this end, we derive a certain limit equation from the original equation at infinity, using a generalized similarity transformation. Through a generalized Cole-Hopf transformation, all the limit equations can be reduced into two typical cases, i.e., $\\Delta u+u^p=0$ and $\\Delta u+e^u=0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-24T07:07:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J25",
      "35B32",
      "35J61",
      "34C10"
    ],
    "keywords": [
      "semilinear elliptic equation",
      "limit equation",
      "general supercritical growth",
      "bifurcation diagrams",
      "study radial solutions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}