Article

 Title: Asymptotic behaviour of solutions of third order nonlinear difference equations of neutral type (English) Author: Andruch-Sobiło, Anna Author: Drozdowicz, Andrzej Language: English Journal: Mathematica Bohemica ISSN: 0862-7959 (print) ISSN: 2464-7136 (online) Volume: 133 Issue: 3 Year: 2008 Pages: 247-258 Summary lang: English . Category: math . Summary: In the paper we consider the difference equation of neutral type $$\Delta ^{3}[x(n)-p(n)x(\sigma (n))] + q(n)f(x(\tau (n)))=0, \quad n \in \Bbb N (n_0),$$ where $p,q\colon\Bbb N(n_0)\rightarrow \Bbb R_+$; $\sigma , \tau \colon\Bbb N\rightarrow \Bbb Z$, $\sigma$ is strictly increasing and $\lim \limits _{n \rightarrow \infty }\sigma (n)=\infty ;$ $\tau$ is nondecreasing and $\lim \limits _{n \rightarrow \infty }\tau (n)=\infty$, $f\colon\Bbb R\rightarrow {\Bbb R}$, $xf(x)>0$. We examine the following two cases: \[ 0

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