On the Dynamics of the Recursive Sequence xn+1 = alpha + xn-k(p)/x(n)(q)

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Gumus M., Ocalan O., Felah N. B.

DISCRETE DYNAMICS IN NATURE AND SOCIETY, cilt.2012, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2012
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1155/2012/241303
  • Dergi Adı: DISCRETE DYNAMICS IN NATURE AND SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Akdeniz Üniversitesi Adresli: Hayır

Özet

We investigate the boundedness character, the oscillatory, and the periodic character of positive solutions of the difference equation x(n+1) = alpha + x(n-k)(p)/x(n)(q), n = 0, 1, . . . , where k is an element of{2, 3 . . .}, alpha, p, q, is an element of (0,infinity) and the initial conditions x(-k), . . . , x(0) are arbitrary positive numbers. We investigate the boundedness character for p is an element of (0,infinity). Also, we investigate the existence of a prime two periodic solution for k is odd. Moreover, when k is even, we prove that there are no prime two periodic solutions of the equation above.