{
  "id": "2304.08238",
  "version": "v1",
  "published": "2023-04-17T12:59:31.000Z",
  "updated": "2023-04-17T12:59:31.000Z",
  "title": "Gradient estimate for solutions of the equation $Δ_pu +av^{q}=0$ on a complete Riemannian manifold",
  "authors": [
    "Jie He",
    "Youde Wang",
    "Guodong Wei"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we use Nash-Moser iteration method to study the local and global behaviours of positive solutions to the nonlinear elliptic equation $\\Delta_pv +av^{q}=0$ defined on a complete Riemannian manifolds $(M,g)$ where $p>1$, $a$ and $q$ are constants. Under some assumptions on $a$, $p$ and $q$, we derive gradient estimates and Liouville type theorems for such positive solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-17T12:59:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete riemannian manifold",
      "nash-moser iteration method",
      "nonlinear elliptic equation",
      "liouville type theorems",
      "positive solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}