A note on the periodicity of the Lyness max equation

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Gelisken A., Cinar C., Karatas R.

ADVANCES IN DIFFERENCE EQUATIONS, cilt.2008, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2008
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1155/2008/651747
  • Dergi Adı: ADVANCES IN DIFFERENCE EQUATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Akdeniz Üniversitesi Adresli: Hayır

Özet

We investigate the periodic nature of solutions of a "max-type" difference equation sometimes referred to as the "Lyness max" equation. The equation we consider is x(n+1) = max{x(n), A}/x(n-1). where A is a positive real parameter, x - 1 = A(r-1), and x(0) = A(ro) such that r(-1) and r(0) are positive rational numbers. The results in this paper answer the Open Problem of Grove and Ladas (2005).