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Title: Asymptotic behavior of solutions of nonlinear difference equations (English)
Author: Migda, Janusz
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959
Volume: 129
Issue: 4
Year: 2004
Pages: 349-359
Summary lang: English
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Category: math
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Summary: The nonlinear difference equation \[ x_{n+1}-x_n=a_n\varphi _n(x_{\sigma (n)})+b_n, \qquad \mathrm{(\text{E})}\] where $(a_n), (b_n)$ are real sequences, $\varphi _n\: \mathbb{R}\longrightarrow \mathbb{R}$, $(\sigma (n))$ is a sequence of integers and $\lim _{n\longrightarrow \infty }\sigma (n)=\infty $, is investigated. Sufficient conditions for the existence of solutions of this equation asymptotically equivalent to the solutions of the equation $y_{n+1}-y_n=b_n$ are given. Sufficient conditions under which for every real constant there exists a solution of equation () convergent to this constant are also obtained. (English)
Keyword: difference equation
Keyword: asymptotic behavior
MSC: 39A10
MSC: 39A11
idZBL: Zbl 1080.39501
idMR: MR2102609
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Date available: 2009-09-24T22:16:11Z
Last updated: 2015-11-01
Stable URL: http://hdl.handle.net/10338.dmlcz/134043
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