{
  "id": "1208.6562",
  "version": "v1",
  "published": "2012-08-31T18:03:49.000Z",
  "updated": "2012-08-31T18:03:49.000Z",
  "title": "Solvability of nonlinear elliptic equations with gradient terms",
  "authors": [
    "Patricio Felmer",
    "Alexander Quaas",
    "Boyan Sirakov"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the solvability in the whole Euclidean space of coercive quasi-linear and fully nonlinear elliptic equations modeled on $\\Delta u\\pm g(|\\nabla u|)= f(u)$, $u\\ge0$, where $f$ and $g$ are increasing continuous functions. We give conditions on $f$ and $g$ which guarantee the availability or the absence of positive solutions of such equations in $\\R^N$. Our results considerably improve the existing ones and are sharp or close to sharp in the model cases. In particular, we completely characterize the solvability of such equations when $f$ and $g$ have power growth at infinity. We also derive a solvability statement for coercive equations in general form.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-31T18:03:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gradient terms",
      "fully nonlinear elliptic equations",
      "euclidean space",
      "model cases",
      "power growth"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.jde.2013.03.003",
      "journal": "Journal of Differential Equations",
      "year": 2013,
      "volume": 254,
      "number": 11,
      "pages": 4327
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013JDE...254.4327F"
    }
  }
}