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 |
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University of Szeged
2018-07-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6650 |
| _version_ | 1797830535993622528 |
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| author | Aleksandra Kapesic |
| author_facet | Aleksandra Kapesic |
| author_sort | Aleksandra Kapesic |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-09T13:37:41Z |
| format | Article |
| id | doaj.art-c940a8b22a024fe39ce58b6bfb761e09 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:41Z |
| publishDate | 2018-07-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-c940a8b22a024fe39ce58b6bfb761e092023-05-09T07:53:08ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752018-07-0120186312310.14232/ejqtde.2018.1.636650Asymptotic representation of intermediate solutions to a cyclic systems of second-order difference equations with regularly varying coefficientsAleksandra Kapesic0University of Niš, Faculty of Science and Mathematics, Department of Mathematics, Niš, SerbiaThe 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.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6650system of difference equationsemden–fowler type difference equationnonlinear difference equationsintermediate solutionsasymptotic behaviorregularly varying sequencediscrete regular variation |
| spellingShingle | Aleksandra Kapesic Asymptotic representation of intermediate solutions to a cyclic systems of second-order difference equations with regularly varying coefficients Electronic Journal of Qualitative Theory of Differential Equations system of difference equations emden–fowler type difference equation nonlinear difference equations intermediate solutions asymptotic behavior regularly varying sequence discrete regular variation |
| title | Asymptotic representation of intermediate solutions to a cyclic systems of second-order difference equations with regularly varying coefficients |
| title_full | Asymptotic representation of intermediate solutions to a cyclic systems of second-order difference equations with regularly varying coefficients |
| title_fullStr | Asymptotic representation of intermediate solutions to a cyclic systems of second-order difference equations with regularly varying coefficients |
| title_full_unstemmed | Asymptotic representation of intermediate solutions to a cyclic systems of second-order difference equations with regularly varying coefficients |
| title_short | Asymptotic representation of intermediate solutions to a cyclic systems of second-order difference equations with regularly varying coefficients |
| title_sort | asymptotic representation of intermediate solutions to a cyclic systems of second order difference equations with regularly varying coefficients |
| topic | system of difference equations emden–fowler type difference equation nonlinear difference equations intermediate solutions asymptotic behavior regularly varying sequence discrete regular variation |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6650 |
| work_keys_str_mv | AT aleksandrakapesic asymptoticrepresentationofintermediatesolutionstoacyclicsystemsofsecondorderdifferenceequationswithregularlyvaryingcoefficients |