Iterative Kneser-Type Criteria for Oscillation of Half-Linear Second-Order Advanced Dynamic Equations

Taher S. Hassan, Bassant M. El-Matary, Ioan-Lucian Popa (), Mouataz Billah Mesmouli, Ismoil Odinaev and Yousef Jawarneh
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Taher S. Hassan: Department of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi Arabia
Bassant M. El-Matary: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Ioan-Lucian Popa: Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania
Mouataz Billah Mesmouli: Department of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi Arabia
Ismoil Odinaev: Department of Automated Electrical Systems, Ural Power Engineering Institute, Ural Federal University, 620002 Yekaterinburg, Russia
Yousef Jawarneh: Department of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi Arabia

Mathematics, 2025, vol. 13, issue 4, 1-13

Abstract: This work aims to develop new iterative Kneser-type criteria for determining the oscillatory behaviour of half-linear second-order advanced dynamic equations on arbitrary unbounded-above time scales T . The results extend and refine previously established criteria for these equations while also generalising classical criteria for corresponding ordinary dynamic equations. This study provides a broader and more flexible approach to analysing such systems by introducing iterative methods. Several examples are included to demonstrate the accuracy, usefulness, and adaptability.

Keywords: oscillation; second order; half-linear; differential equations; dynamic equations; time scales (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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