Nonoscillatory solutions of the four-dimensional difference system
We study asymptotic properties of nonoscillatory solutions for a four-dimensional system \[\begin{aligned} \Delta x_{n}&= C_{n}\, y_{n}^{\frac{1}{\gamma}} \\ \Delta y_{n}&= B_{n}\, z_{n}^{\frac{1}{\beta}} \\ \Delta z_{n}&= A_{n}\, w_{n}^{\frac{1}{\alpha}} \\ \Delta w_{n}&= D_{n}\, x_...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2012-05-01
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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=1108 |
| _version_ | 1797830673861443584 |
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| author | Zuzana Dosla J. Krejčová |
| author_facet | Zuzana Dosla J. Krejčová |
| author_sort | Zuzana Dosla |
| collection | DOAJ |
| description | We study asymptotic properties of nonoscillatory solutions for a four-dimensional system
\[\begin{aligned}
\Delta x_{n}&= C_{n}\, y_{n}^{\frac{1}{\gamma}} \\
\Delta y_{n}&= B_{n}\, z_{n}^{\frac{1}{\beta}} \\
\Delta z_{n}&= A_{n}\, w_{n}^{\frac{1}{\alpha}} \\
\Delta w_{n}&= D_{n}\, x_{n+\tau}^{\delta}.
\end{aligned}\]
In particular, we give sufficient conditions that any bounded nonoscillatory solution tends to zero and any unbounded nonoscillatory solution tends to infinity in all its components. |
| first_indexed | 2024-04-09T13:40:54Z |
| format | Article |
| id | doaj.art-c49f64b0ab3344b9b184c0fd33d638ef |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:40:54Z |
| publishDate | 2012-05-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-c49f64b0ab3344b9b184c0fd33d638ef2023-05-09T07:53:02ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752012-05-012012411110.14232/ejqtde.2012.3.41108Nonoscillatory solutions of the four-dimensional difference systemZuzana Dosla0J. Krejčová1Masaryk University, Brno, Czech RepublicMasaryk University, Brno, Czech RepublicWe study asymptotic properties of nonoscillatory solutions for a four-dimensional system \[\begin{aligned} \Delta x_{n}&= C_{n}\, y_{n}^{\frac{1}{\gamma}} \\ \Delta y_{n}&= B_{n}\, z_{n}^{\frac{1}{\beta}} \\ \Delta z_{n}&= A_{n}\, w_{n}^{\frac{1}{\alpha}} \\ \Delta w_{n}&= D_{n}\, x_{n+\tau}^{\delta}. \end{aligned}\] In particular, we give sufficient conditions that any bounded nonoscillatory solution tends to zero and any unbounded nonoscillatory solution tends to infinity in all its components.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1108asymptotic propertiesdifference equationkneser solutionstrongly monotone solution |
| spellingShingle | Zuzana Dosla J. Krejčová Nonoscillatory solutions of the four-dimensional difference system Electronic Journal of Qualitative Theory of Differential Equations asymptotic properties difference equation kneser solution strongly monotone solution |
| title | Nonoscillatory solutions of the four-dimensional difference system |
| title_full | Nonoscillatory solutions of the four-dimensional difference system |
| title_fullStr | Nonoscillatory solutions of the four-dimensional difference system |
| title_full_unstemmed | Nonoscillatory solutions of the four-dimensional difference system |
| title_short | Nonoscillatory solutions of the four-dimensional difference system |
| title_sort | nonoscillatory solutions of the four dimensional difference system |
| topic | asymptotic properties difference equation kneser solution strongly monotone solution |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1108 |
| work_keys_str_mv | AT zuzanadosla nonoscillatorysolutionsofthefourdimensionaldifferencesystem AT jkrejcova nonoscillatorysolutionsofthefourdimensionaldifferencesystem |