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Karakostas, G. L.; Stević, S.

Slowly varying solutions of the difference equation \(x_{n+1}=f(x_n, \dots, x_{n-k})+g(n,x_n,x_{n-1},\dots,x_{n-k})\). (English) Zbl 1048.39003

J. Difference Equ. Appl. 10, No. 3, 249-255 (2004).
The authors obtain sufficient conditions which guarantee that all bounded solutions of the difference equation \[ x_{n+1}=f(x_n,\ldots,x_{n-k})+g(n, x_n,x_{n-1},\ldots,x_{n-k}) \] are slowly varying in the sense that \(\lim (x_{n+1}-x_n)=0\).
Reviewer: Mingshu Peng (Beijing)

Cited in 4 Documents

MSC:

39A11 Stability of difference equations (MSC2000)

Keywords:

slowly varying solution; bounded solutions; difference equation; full orbit
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Full Text: DOI

References:

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