{
  "id": "1107.5783",
  "version": "v1",
  "published": "2011-07-28T18:11:52.000Z",
  "updated": "2011-07-28T18:11:52.000Z",
  "title": "Numerical analysis of semilinear elliptic equations with finite spectral interaction",
  "authors": [
    "José Cal Neto",
    "Carlos Tomei"
  ],
  "comment": "20 pages, 15 figures (34 .eps files)",
  "categories": [
    "math.AP",
    "math.FA",
    "math.NA"
  ],
  "abstract": "We present an algorithm to solve $- \\lap u - f(x,u) = g$ with Dirichlet boundary conditions in a bounded domain $\\Omega$. The nonlinearities are non-resonant and have finite spectral interaction: no eigenvalue of $-\\lap_D$ is an endpoint of $\\bar{\\partial_2f(\\Omega,\\RR)}$, which in turn only contains a finite number of eigenvalues. The algorithm is based in ideas used by Berger and Podolak to provide a geometric proof of the Ambrosetti-Prodi theorem and advances work by Smiley and Chun for the same problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-07-28T18:11:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B32",
      "35J91",
      "65N30"
    ],
    "keywords": [
      "finite spectral interaction",
      "semilinear elliptic equations",
      "numerical analysis",
      "dirichlet boundary conditions",
      "eigenvalue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.5783C"
    }
  }
}