{
  "id": "1810.03934",
  "version": "v1",
  "published": "2018-10-09T12:19:13.000Z",
  "updated": "2018-10-09T12:19:13.000Z",
  "title": "Existence and uniqueness of the p-generalized modified error function",
  "authors": [
    "Julieta Bollati",
    "María F. Natale",
    "José A. Semitiel",
    "Domingo A. Tarzia"
  ],
  "comment": "7 pages, 0 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper, the p-generalized modified error function is defined as the solution to a non-linear ordinary differential problem of second order with a Robin type condition at $x=0$. Existence and uniqueness of a non-negative analytic solution is proved by using a fixed point strategy. It is shown that the p-generalized modified error function converges to the p-modified error function defined as the solution to a similar problem with a Dirichlet condition at x=0. In both problems, for p=1, the generalized modified error function and the modified error function, studied recently in literature, are recovered",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-09T12:19:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uniqueness",
      "non-linear ordinary differential problem",
      "robin type condition",
      "p-generalized modified error function converges",
      "fixed point strategy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}