Second-order advanced dynamic equations on time scales: Oscillation analysis via monotonicity properties - Samy E. Affan; Elmetwally M. Elabbasy; Bassant M. El-Matary; Taher S. Hassan; Ahmed M. Hassan (AIMS Mathematics)
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(ζ(\ell) \varkappa^{Δ}(\ell)\right)^{Δ} + 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.