On the recursive sequence \(x_{n+1}=\frac A{x_n}+\frac 1{x_{n-2}}\). (English) Zbl 0904.39012
The authors establish that every positive solution of the equation
\[
x_{n+1}= \frac{A}{x_n}+ {1}{x_{n-2}},\quad n= 0,1,\ldots,
\]
where \(x_{-1}\),\(x_{-2}\), \(A\in(0,\infty)\), converges to a period two solution. This proves Conjecture 2.4.2 of G. Ladas [J. Differ. Equ. Appl. 2, 449–452 (1996; 10.1080/10236199608808079)].
Reviewer: E.Thandapani (Salem)
MSC:
| 39A12 | Discrete version of topics in analysis |
| 39A10 | Additive difference equations |
| 39A30 | Stability theory for difference equations |
