## On the difference equation $$X_{n+1} = \alpha + \frac{x_{n-1}}{x_n}$$.(English)Zbl 1155.39305

Summary: We study the behavior of the solutions of the difference equation $x_{n+1} = \alpha + \frac{x_{n-1}}{x_n}\quad n=0,1,\dots$ where $$\alpha$$ is a negative number. Included are results which considerably improve and correct those in the recently published paper [A.E. Hamza, J. Math. Anal. Appl. 322, No. 2, 668–674 (2006; Zbl 1105.39008)]. We also refute Conjecture 2 in [G. Ladas et al., J. Difference Equ. Appl. 7, No. 3, 477–482 (2001; Zbl 1081.39503)].

### MSC:

 39A23 Periodic solutions of difference equations

### Citations:

Zbl 1105.39008; Zbl 1081.39503
Full Text:

### References:

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