{
  "id": "2005.14377",
  "version": "v1",
  "published": "2020-05-29T04:19:38.000Z",
  "updated": "2020-05-29T04:19:38.000Z",
  "title": "Quasilinear elliptic equations with sub-natural growth terms in bounded domains",
  "authors": [
    "Takanobu Hara"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the existence of positive solutions to weighted quasilinear elliptic differential equations of the type \\[ \\begin{cases} - \\Delta_{p, w} u = \\sigma u^{q} & \\text{in $\\Omega$}, \\\\ u = 0 & \\text{on $\\partial \\Omega$} \\end{cases} \\] in the sub-natural growth case $0 < q < p - 1$, where $\\Omega$ is a bounded domain in $\\mathbb{R}^{n}$, $\\Delta_{p, w}$ is a weighted $p$-Laplacian, and $\\sigma$ is a Radon measure on $\\Omega$. We give criteria for the existence problem. For the proof, we investigate various properties of $p$-superharmonic functions, especially solvability of Dirichlet problems with non-finite measure data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-29T04:19:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J92",
      "35J20",
      "42B37"
    ],
    "keywords": [
      "quasilinear elliptic equations",
      "sub-natural growth terms",
      "bounded domain",
      "weighted quasilinear elliptic differential equations",
      "sub-natural growth case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}