An explicit formula and forbidden set for a higher order difference equation
Mehmet Gumus, Raafat Abo-Zeid
article (Uluslararası, Hakemli) | Yazar(lar): Mehmet Gumus, Raafat Abo-Zeid | Yıl: 2020 | Dergi/Kurum: JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | İndeks: WOS.SCI | DOI: 10.1007/s12190-019-01311-9 | Anahtar Kelimeler: Difference equation, Forbidden set, Periodic solution, Unbounded solution — Özet: In this paper, we
In this paper, we determine the forbidden set, introduce an explicit formula for the solutions and discuss the global behavior of solutions of the difference equation
x(n+1) ax(n)x(n)-k+1/bx(n-k)+1 + cx(n-k,) n = 0, 1, ...,
where a, b, c are positive real numbers, the initial conditions x(-k), x(-k+1),..., x(-1), x(0) are real numbers and k is a positive integer.