{
  "id": "2003.11186",
  "version": "v1",
  "published": "2020-03-25T02:30:32.000Z",
  "updated": "2020-03-25T02:30:32.000Z",
  "title": "Existence of minimal solutions to quasilinear elliptic equations with several sub-natural growth terms",
  "authors": [
    "Takanobu Hara",
    "Adisak Seesanea"
  ],
  "comment": "Published online in Nonlinear Analysis",
  "doi": "10.1016/j.na.2020.111847",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the existence of positive solutions to quasilinear elliptic equations of the type \\[ -\\Delta_{p} u = \\sigma u^{q} + \\mu \\quad \\text{in} \\ \\mathbb{R}^{n}, \\] in the sub-natural growth case $0 < q < p - 1$, where $\\Delta_{p}u = \\nabla \\cdot ( |\\nabla u|^{p - 2} \\nabla u )$ is the $p$-Laplacian with $1 < p < n$, and $\\sigma$ and $\\mu$ are nonnegative Radon measures on $\\mathbb{R}^{n}$. We construct minimal generalized solutions under certain generalized energy conditions on $\\sigma$ and $\\mu$. To prove this, we give new estimates for interaction between measures. We also construct solutions to equations with several sub-natural growth terms using the same methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-25T02:30:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J92",
      "35J20",
      "42B37"
    ],
    "keywords": [
      "quasilinear elliptic equations",
      "sub-natural growth terms",
      "minimal solutions",
      "sub-natural growth case",
      "construct minimal generalized solutions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}