{
  "id": "1808.06561",
  "version": "v1",
  "published": "2018-08-20T16:41:58.000Z",
  "updated": "2018-08-20T16:41:58.000Z",
  "title": "Existence and nonexistence of positive solutions of quasi-linear elliptic equations with gradient terms",
  "authors": [
    "Dania Morales"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the existence and nonexistence of positive solutions in the whole Euclidean space of coercive quasi-linear elliptic equations such as \\[ \\Delta_p u = f(u)\\pm g(\\left|\\nabla u\\right|) \\] where $f\\in C([0,\\infty))$ and $g\\in C^{0,1}([0,\\infty)) $ are strictly increasing with $ f(0)=g(0)=0$. Among other things we obtain generalized integral conditions of Keller-Osserman type. In the particular case of plus sign on the right-hand side we obtain that different conditions are needed when $p\\geq 2$ or $p\\leq 2$, due to the degeneracy of the operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-20T16:41:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive solutions",
      "gradient terms",
      "nonexistence",
      "coercive quasi-linear elliptic equations",
      "plus sign"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}