Oscillation of a second order half-linear difference equation and the discrete Hardy inequality
In local terms on finite and infinite intervals we obtain necessary and sufficient conditions for the conjugacy and disconjugacy of the following second order half-linear difference equation \begin{equation*} \Delta(\rho_i|\Delta y_i|^{p-2}\Delta y_i)+v_i|y_{i+1}|^{p-2}y_{i+1}=0, \qquad i=0, 1, 2,\d...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2017-05-01
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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=5361 |
| _version_ | 1797830571823464448 |
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| author | Aigerim Kalybay Danagul Karatayeva Ryskul. Oinarov Ainur Temirkhanova |
| author_facet | Aigerim Kalybay Danagul Karatayeva Ryskul. Oinarov Ainur Temirkhanova |
| author_sort | Aigerim Kalybay |
| collection | DOAJ |
| description | In local terms on finite and infinite intervals we obtain necessary and sufficient conditions for the conjugacy and disconjugacy of the following second order half-linear difference equation
\begin{equation*}
\Delta(\rho_i|\Delta y_i|^{p-2}\Delta y_i)+v_i|y_{i+1}|^{p-2}y_{i+1}=0, \qquad i=0, 1, 2,\dots,
\end{equation*}
where $1<p<\infty$, $\Delta y_i=y_{i+1}-y_i$, $\{\rho_i\}$ and $\{v_i\}$ are sequences of positive and non-negative real numbers, respectively. Moreover, we study oscillation and non-oscillation properties of this equation. |
| first_indexed | 2024-04-09T13:38:13Z |
| format | Article |
| id | doaj.art-49e41f0b4585408db839cef99b9c335b |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:38:13Z |
| publishDate | 2017-05-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-49e41f0b4585408db839cef99b9c335b2023-05-09T07:53:07ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752017-05-0120174311610.14232/ejqtde.2017.1.435361Oscillation of a second order half-linear difference equation and the discrete Hardy inequalityAigerim Kalybay0Danagul Karatayeva1Ryskul. Oinarov2Ainur Temirkhanova3KIMEP University, Almaty, KazakhstanL. N. Gumilyov Eurasian National University, Astana, KazakhstanL. N. Gumilyov Eurasian National University, Astana, KazakhstanL. N. Gumilyov Eurasian National University, Astana, KazakhstanIn local terms on finite and infinite intervals we obtain necessary and sufficient conditions for the conjugacy and disconjugacy of the following second order half-linear difference equation \begin{equation*} \Delta(\rho_i|\Delta y_i|^{p-2}\Delta y_i)+v_i|y_{i+1}|^{p-2}y_{i+1}=0, \qquad i=0, 1, 2,\dots, \end{equation*} where $1<p<\infty$, $\Delta y_i=y_{i+1}-y_i$, $\{\rho_i\}$ and $\{v_i\}$ are sequences of positive and non-negative real numbers, respectively. Moreover, we study oscillation and non-oscillation properties of this equation.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5361half-linear equationconjugatedisconjugateoscillationnon-oscillationdiscrete hardy inequality |
| spellingShingle | Aigerim Kalybay Danagul Karatayeva Ryskul. Oinarov Ainur Temirkhanova Oscillation of a second order half-linear difference equation and the discrete Hardy inequality Electronic Journal of Qualitative Theory of Differential Equations half-linear equation conjugate disconjugate oscillation non-oscillation discrete hardy inequality |
| title | Oscillation of a second order half-linear difference equation and the discrete Hardy inequality |
| title_full | Oscillation of a second order half-linear difference equation and the discrete Hardy inequality |
| title_fullStr | Oscillation of a second order half-linear difference equation and the discrete Hardy inequality |
| title_full_unstemmed | Oscillation of a second order half-linear difference equation and the discrete Hardy inequality |
| title_short | Oscillation of a second order half-linear difference equation and the discrete Hardy inequality |
| title_sort | oscillation of a second order half linear difference equation and the discrete hardy inequality |
| topic | half-linear equation conjugate disconjugate oscillation non-oscillation discrete hardy inequality |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5361 |
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