{
  "id": "1404.5751",
  "version": "v1",
  "published": "2014-04-23T09:04:29.000Z",
  "updated": "2014-04-23T09:04:29.000Z",
  "title": "Existence and non-existence of Blow-up solutions for a non-autonomous problem with indefinite and gradient terms",
  "authors": [
    "Claudianor O. Alves",
    "Carlos A. Santos",
    "Jiazheng Zhou"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We deal with existence and non-existence of non-negative entire solutions that blow-up at infinity for a quasilinear problem depending on a non-negative real parameter. Our main objectives in this paper are to provide far more general conditions for existence and non-existence of solutions. To this end, we explore an associated $\\mu$-parameter convective ground state problem, sub and super solutions method combined and an approximation arguments to show existence of solutions. To show the result of non-existence of solutions, we follow an idea due to Mitidieri-Pohozaev.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-23T09:04:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "blow-up solutions",
      "gradient terms",
      "non-existence",
      "non-autonomous problem",
      "parameter convective ground state problem"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00033-014-0451-4",
      "journal": "Zeitschrift Angewandte Mathematik und Physik",
      "year": 2015,
      "month": "Jun",
      "pages": 891,
      "volume": 66,
      "number": 3
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015ZaMP...66..891A"
    }
  }
}