{
  "id": "0812.3398",
  "version": "v1",
  "published": "2008-12-17T21:03:45.000Z",
  "updated": "2008-12-17T21:03:45.000Z",
  "title": "Global Attractivity of the Equilibrium of a Difference Equation: An Elementary Proof Assisted by Computer Algebra System",
  "authors": [
    "Orlando Merino"
  ],
  "comment": "10 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $p$ and $q$ be arbitrary positive numbers. It is shown that if $q < p$, then all solutions to the difference equation \\tag{E} x_{n+1} = \\frac{p+q x_n}{1+x_{n-1}}, \\quad n=0,1,2,..., \\quad x_{-1}>0, x_0>0 converge to the positive equilibrium $\\overline{x} = {1/2}(q-1 + \\sqrt{(q-1)^2 + 4 p})$. \\medskip The above result, taken together with the 1993 result of Koci\\'c and Ladas for equation (E) with $q \\geq p$, gives global attractivity of the positive equilibrium of (E) for all positive values of the parameters, thus completing the proof of a conjecture of Ladas.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-12-17T21:03:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39A11"
    ],
    "keywords": [
      "computer algebra system",
      "difference equation",
      "global attractivity",
      "elementary proof",
      "positive equilibrium"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.3398M"
    }
  }
}