Asymptotic representation of intermediate solutions to a cyclic systems of second-order difference equations with regularly varying coefficients
The cyclic system of second-order difference equations \begin{equation*} \Delta(p_i(n)|\Delta x_i(n)|^{\alpha_i-1}\Delta x_i(n)) = q_i(n)|x_{i+1}(n+1)|^{\beta_i-1}x_{i+1}(n+1), \end{equation*} for $i=\overline{1,N}$ where $x_{N+1}=x_1,$ is analysed in the framework of discrete regular variation. Und...
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2018-07-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6650 |
| Summary: | The cyclic system of second-order difference equations
\begin{equation*}
\Delta(p_i(n)|\Delta x_i(n)|^{\alpha_i-1}\Delta x_i(n)) = q_i(n)|x_{i+1}(n+1)|^{\beta_i-1}x_{i+1}(n+1),
\end{equation*}
for $i=\overline{1,N}$ where $x_{N+1}=x_1,$ is analysed in the framework of discrete regular variation. Under the assumption that $\alpha_i$ and $\beta_i$ are positive constants such that $\alpha_1\alpha_2\cdots\alpha_N>\beta_1\beta_2\cdots\beta_N$ and $p_i$ and $q_i$ are regularly varying sequences it is shown that the situation in which this system possesses regularly varying intermediate solutions can be completely characterized. Besides, precise information can be acquired about the asymptotic behavior at infinity of these solutions. |
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| ISSN: | 1417-3875 |