{
  "id": "2311.13179",
  "version": "v1",
  "published": "2023-11-22T06:05:14.000Z",
  "updated": "2023-11-22T06:05:14.000Z",
  "title": "On the non-existence of positive solutions to a class of quasilinear elliptic equations on complete Riemannian manifolds",
  "authors": [
    "Jie He",
    "Youde Wang"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2311.02568",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper uses Nash-Moser iteration method to study solutions to the nonlinear elliptic equation $\\Delta_pv+b|\\nabla v|^q+cv^r =0$ on a complete Riemannian manifold $(M,g)$, where $b, c, p, q$ and $r$ are constants. When $b$ and $c$ have the same sign, we give some regions of $(q, r)$ where the Cheng-Yau type gradient estimate holds. By generalizing some results of \\cite{MR1879326} to manifold, we obtain a more wider range of $(q,r)$ for Liouville properties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-22T06:05:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete riemannian manifold",
      "quasilinear elliptic equations",
      "positive solutions",
      "cheng-yau type gradient estimate holds",
      "non-existence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}