{
  "id": "2203.13113",
  "version": "v1",
  "published": "2022-03-24T15:13:26.000Z",
  "updated": "2022-03-24T15:13:26.000Z",
  "title": "Estimates of Nonnegative Solutions to Semilinear Elliptic Equations",
  "authors": [
    "Khalifa El Mabrouk",
    "Basma Nayli"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $L$ be a second order uniformly elliptic differential operator in a domain $D$ of $\\mathbb{R}^{d}$, $\\psi:\\mathbb{R}_+\\to \\mathbb{R}_+$ be a nondecreasing continuous function and let $\\xi,g:D\\to\\mathbb{R}_+$ be locally bounded Borel measurable functions. Under appropriate conditions, we determine a function $\\varphi$ with values in $]0,1]$ such that for every nonnegative solution to inequality $-Lu+\\xi\\psi(u) \\geq g$ in $D$ and for every $x\\in D$, $$ u(x)\\geq p(x)\\,\\varphi\\left(\\frac{G_D(\\xi\\psi(p))(x)}{p(x)}\\right) $$ where $p=G_Dg$ is the Green function of $g$. The function $\\varphi$ is completely determined by $\\psi$ and does not depend on $L,D,\\xi$ or $g$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-24T15:13:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J61",
      "35B45",
      "31B10"
    ],
    "keywords": [
      "semilinear elliptic equations",
      "nonnegative solution",
      "bounded borel measurable functions",
      "second order uniformly elliptic differential",
      "order uniformly elliptic differential operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}