{
  "id": "math/0410452",
  "version": "v2",
  "published": "2004-10-20T21:19:14.000Z",
  "updated": "2005-03-01T19:22:04.000Z",
  "title": "Existence of a solution to a nonlinear equation",
  "authors": [
    "A. G. Ramm"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Equation $(-\\Delta+k^2)u+f(u)=0$ in $D$, $u\\mid_{\\partial D}=0$, where $k=\\const>0$ and $D\\subset\\R^3$ is a bounded domain, has a solution if $f:\\R\\to\\R$ is a continuous function in the region $|u|\\geq a$, piecewise-continuous in the region $|u|\\leq a$, with finitely many discontinuity points $u_j$ such that $f(u_j\\pm 0)$ exist, and $uf(y)\\geq 0$ for $|u|\\geq a$, where $a\\geq 0$ is an arbitrary fixed number.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-03-01T19:22:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J65"
    ],
    "keywords": [
      "nonlinear equation",
      "discontinuity points",
      "arbitrary fixed number",
      "bounded domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10452R"
    }
  }
}