On the Dynamics of the Recursive Sequence <i>xn</i>+1 = α + <i>xn</i>-<i>k<SUP>p</SUP></i>/x<sub>n</sub><SUP>q</SUP>
Mehmet Gumus, Ozkan Ocalan, Nilufer B. Felah
article (Uluslararası, Hakemli) | Yazar(lar): Mehmet Gumus, Ozkan Ocalan, Nilufer B. Felah | Yıl: 2012 | Dergi/Kurum: DISCRETE DYNAMICS IN NATURE AND SOCIETY | İndeks: WOS.SCI | DOI: 10.1155/2012/241303 — Özet: We investigate the boundedness character, the oscillatory, and the periodic character of positive solutions o
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.