## On a difference equation with 3-periodic coefficient.(English)Zbl 1086.39011

Let $$(p_n)$$ be a positive sequence of period 3. The authors study the periodicity, the boundedness and the asymptotic behavior of the positive solutions of the non-autonomous difference equation $x_{n+1} = p_n + {x_{n-1} \over x_n}, \quad n=0, 1, \dots.$ They find a new condition for the global attractivity result proved by R. Devault, V. L. Kocic and D. Stutson [J. Difference Equ. Appl. 11, No. 8, 707–719 (2005; Zbl 1079.39005)].

### MSC:

 39A11 Stability of difference equations (MSC2000) 39A20 Multiplicative and other generalized difference equations

Zbl 1079.39005
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### References:

 [1] DOI: 10.1006/jmaa.1999.6346 · Zbl 0962.39004 [2] DOI: 10.1080/10236199708808120 · Zbl 0905.39003 [3] DOI: 10.1080/10236190108808308 · Zbl 1002.39003 [4] DOI: 10.1080/1023619021000053980 · Zbl 1023.39013 [5] DOI: 10.1080/10236190500137405 · Zbl 1079.39005 [6] Kocic V.L., Global Behavior of Nonlinear Difference Equations of Higher Order with Applications (1993) · Zbl 0787.39001 [7] Kuczma M., Iterative Functional Equations. Encyclopedia of Mathematics and its Applications (1990) [8] DOI: 10.1080/10236190410001731434 · Zbl 1061.39006 [9] DOI: 10.1080/10236190500035310 · Zbl 1074.39010
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