Second-order advanced dynamic equations on time scales: Oscillation analysis via monotonicity properties
This paper derives new oscillation criteria for a class of second-order non-canonical advanced dynamic equations of the form \begin{document}$ \begin{equation*} \left(\zeta(\ell) \varkappa^{\Delta}(\ell)\right)^{\Delta} + q (\ell) \varkappa(\wp(\ell)) = 0. \end{equation*} $\end{document} The deriv...
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| Format: | Article |
| Language: | English |
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AIMS Press
2025-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025206 |
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| author | Samy E. Affan Elmetwally M. Elabbasy Bassant M. El-Matary Taher S. Hassan Ahmed M. Hassan |
| author_facet | Samy E. Affan Elmetwally M. Elabbasy Bassant M. El-Matary Taher S. Hassan Ahmed M. Hassan |
| author_sort | Samy E. Affan |
| collection | DOAJ |
| description | This paper derives new oscillation criteria for a class of second-order non-canonical advanced dynamic equations of the form \begin{document}$ \begin{equation*} \left(\zeta(\ell) \varkappa^{\Delta}(\ell)\right)^{\Delta} + q (\ell) \varkappa(\wp(\ell)) = 0. \end{equation*} $\end{document} The derived results are based on establishing dynamic inequalities, which lead to novel monotonicity properties of the solutions. These properties are then used to derive new oscillatory conditions. This approach has been successfully applied to difference and differential equations due to the sharpness of its criteria. However, no analogous studies have adopted a similar methodology for dynamic equations on time scales. Furthermore, this study includes examples to illustrate the importance and sharpness of the main results. |
| format | Article |
| id | doaj-art-be2ef0f4e7264252bd29aa171632d5b2 |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-be2ef0f4e7264252bd29aa171632d5b22025-08-20T02:08:20ZengAIMS PressAIMS Mathematics2473-69882025-02-011024473449110.3934/math.2025206Second-order advanced dynamic equations on time scales: Oscillation analysis via monotonicity propertiesSamy E. Affan0Elmetwally M. Elabbasy1Bassant M. El-Matary2Taher S. Hassan3Ahmed M. Hassan4Department of Mathematics, Faculty of Science, Benha University, Benha-Kalubia 13518, EgyptDepartment of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptDepartment of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi ArabiaDepartment of Mathematics, College of Science, University of Hail, Hail 2440, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Benha University, Benha-Kalubia 13518, EgyptThis paper derives new oscillation criteria for a class of second-order non-canonical advanced dynamic equations of the form \begin{document}$ \begin{equation*} \left(\zeta(\ell) \varkappa^{\Delta}(\ell)\right)^{\Delta} + q (\ell) \varkappa(\wp(\ell)) = 0. \end{equation*} $\end{document} The derived results are based on establishing dynamic inequalities, which lead to novel monotonicity properties of the solutions. These properties are then used to derive new oscillatory conditions. This approach has been successfully applied to difference and differential equations due to the sharpness of its criteria. However, no analogous studies have adopted a similar methodology for dynamic equations on time scales. Furthermore, this study includes examples to illustrate the importance and sharpness of the main results.https://www.aimspress.com/article/doi/10.3934/math.2025206kneser-typesharposcillationnon-canonicaladvanceddynamic equationsdifferential equationsmonotonicity properties |
| spellingShingle | Samy E. Affan Elmetwally M. Elabbasy Bassant M. El-Matary Taher S. Hassan Ahmed M. Hassan Second-order advanced dynamic equations on time scales: Oscillation analysis via monotonicity properties AIMS Mathematics kneser-type sharp oscillation non-canonical advanced dynamic equations differential equations monotonicity properties |
| title | Second-order advanced dynamic equations on time scales: Oscillation analysis via monotonicity properties |
| title_full | Second-order advanced dynamic equations on time scales: Oscillation analysis via monotonicity properties |
| title_fullStr | Second-order advanced dynamic equations on time scales: Oscillation analysis via monotonicity properties |
| title_full_unstemmed | Second-order advanced dynamic equations on time scales: Oscillation analysis via monotonicity properties |
| title_short | Second-order advanced dynamic equations on time scales: Oscillation analysis via monotonicity properties |
| title_sort | second order advanced dynamic equations on time scales oscillation analysis via monotonicity properties |
| topic | kneser-type sharp oscillation non-canonical advanced dynamic equations differential equations monotonicity properties |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025206 |
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