On rational recursive sequences. (English) Zbl 0777.39002

Kocic, V. L.; Ladas, G.; Rodrigues, I. W.

J. Math. Anal. Appl. 173, No. 1, 127-157 (1993).

The present study is related to the global asymptotic behavior, the oscillatory character and the periodic nature of all solutions of the rational recursive sequences;
\(x_{n+1}=[a+\sum^{k-1}_{i=0}b_ ix_{n-i}]/x_{n-k}\), and \(x_{n+1}=(a+bx_ n)/(A+x_{n-k})\), \(n=0,1,2,\dots\), which arises due to an open problem [problem # 1343, Math., Mag. 63, No. 2, 125 (1990)].

Reviewer: B.M.Agrawal (Lashkar-Gwalior)

MSC:

39A10	Additive difference equations
39A11	Stability of difference equations (MSC2000)

Keywords:

periodic solutions; global asymptotic behavior; oscillatory character; rational recursive sequences