{
  "id": "2204.08061",
  "version": "v1",
  "published": "2022-04-17T18:07:32.000Z",
  "updated": "2022-04-17T18:07:32.000Z",
  "title": "Positive solutions of quasilinear elliptic equations with Fuchsian potentials in Wolff class",
  "authors": [
    "Ratan Kr. Giri",
    "Yehuda Pinchover"
  ],
  "comment": "40 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "Using Harnack's inequality and a scaling argument we study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point $\\zeta \\in \\partial\\Omega\\cup\\{\\infty\\}$ for the quasilinear elliptic equation $$-\\text{div}(|\\nabla u|_A^{p-2}A\\nabla u)+V|u|^{p-2}u =0\\quad\\text{ in } \\Omega,$$ where $\\Omega$ is a domain in $\\mathbb{R}^d$, $d\\geq 2$, $1<p<d$, and $A=(a_{ij})\\in L_{\\rm loc}^{\\infty}(\\Omega; \\mathbb{R}^{d\\times d})$ is a symmetric and locally uniformly positive definite matrix. It is assumed that the potential $V$ belongs to a certain Wolff class and has a generalized Fuchsian-type singularity at an isolated point $\\zeta\\in \\partial \\Omega \\cup \\{\\infty\\}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-17T18:07:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B53",
      "35B09",
      "35J62",
      "35B40"
    ],
    "keywords": [
      "quasilinear elliptic equation",
      "wolff class",
      "positive solutions",
      "fuchsian potentials",
      "uniformly positive definite matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}