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MATHEMATICA BOHEMICA, Vol. 129, No. 4, pp. 349-359 (2004)
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Asymptotic behavior of solutions of nonlinear difference equations

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Janusz Migda

* Janusz Migda*, Faculty of Mathematics & Computer Science, A. Mickiewicz University, ul. Umultowska 87, 61-614 Poznan, Poland, e-mail: ` migda@amu.edu.pl`

**Abstract:** The nonlinear difference equation

\label{E} x_{n+1}-x_n=a_n\varphi_n(x_{\sigma(n)})+b_n, \tag{$\text E$}

where $(a_n), (b_n)$ are real sequences, $\varphi_n \Bbb R\longrightarrow\Bbb R$, $(\sigma(n))$ 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 (\ref{E}) convergent to this constant are also obtained.

**Keywords:** difference equation, asymptotic behavior

**Classification (MSC2000):** 39A10

**Full text of the article:**

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