{
  "id": "1512.02716",
  "version": "v1",
  "published": "2015-12-09T01:37:55.000Z",
  "updated": "2015-12-09T01:37:55.000Z",
  "title": "On Two Nonlinear Difference Equations",
  "authors": [
    "Julius Fergy T. Rabago",
    "Jerico B. Bacani"
  ],
  "comment": "The first version of the paper has been drafted on March 24, 2014",
  "categories": [
    "math.DS"
  ],
  "abstract": "The behavior of solutions of the following nonlinear difference equations \\[ x_{n+1}=\\displaystyle\\frac{q}{p+x_n^{\\nu}} \\quad \\text{and} \\quad y_{n+1}=\\displaystyle\\frac{q}{-p+y_n^{\\nu}}, \\] where $p, q \\in\\mathbb{R}^+$ and $\\nu\\in \\mathbb{N}$ are studied. The solution form of these two equations when $\\nu =1$ are expressed in terms of Horadam numbers. Furthermore, the behavior of their solutions are investigated for all integer $\\nu > 0$ and several numerical examples are presented to illustrate the results exhibited. The present work generalizes those seen in [{\\it Adv. Differ. Equ.}, {\\bf 2013}:174 (2013), 7 pages].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-09T01:37:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39A10",
      "11B39"
    ],
    "keywords": [
      "nonlinear difference equations",
      "horadam numbers",
      "solution form",
      "work generalizes",
      "numerical examples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}