Enhanced Kneser-type oscillation criteria for second-order functional quasilinear dynamic equations on time scales

Taher S. Hassan; Elvan Akın; Bassant M. El-Matary; Ioan-Lucian Popa; Mouataz Billah Mesmouli; Ismoil Odinaev; Akbar Ali; Taher S. Hassan; Elvan Akın; Bassant M. El-Matary; Ioan-Lucian Popa; Mouataz Billah Mesmouli; Ismoil Odinaev; Akbar Ali

doi:10.3934/math.20251057

AIMS Mathematics

2025, Volume 10, Issue 10: 23789-23802. doi: 10.3934/math.20251057

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Enhanced Kneser-type oscillation criteria for second-order functional quasilinear dynamic equations on time scales

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il, 2440, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt
3.
Jadara University Research Center, Jadara University, Irbid 21110, Jordan
4.
Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65401, USA
5.
Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia
6.
Department of Computing, Mathematics and Electronics, 1 Decembrie 1918 University of Alba Iulia, 510009 Alba Iulia, Romania
7.
Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania
8.
Department of Automated Electrical Systems, Ural Power Engineering Institute, Ural Federal University, 620002 Yekaterinburg, Russia

Received: 20 February 2025 Revised: 22 July 2025 Accepted: 30 July 2025 Published: 20 October 2025
MSC : 26E70, 34C10, 34K11, 34K42, 34N05

This work presents new Kneser-type oscillation criteria for second-order quasilinear functional dynamic equations defined on arbitrary unbounded above time scales. Our approach employs the Riccati transformation technique in conjunction with the integral averaging method. The results show a significant improvement over recent Kneser-type oscillation criteria. We provided several illustrative examples to highlight the importance of our findings.
- oscillation,
- Kneser-type,
- quasilinear,
- differential equations,
- dynamic equations,
- time scales
Citation: Taher S. Hassan, Elvan Akın, Bassant M. El-Matary, Ioan-Lucian Popa, Mouataz Billah Mesmouli, Ismoil Odinaev, Akbar Ali. Enhanced Kneser-type oscillation criteria for second-order functional quasilinear dynamic equations on time scales[J]. AIMS Mathematics, 2025, 10(10): 23789-23802. doi: 10.3934/math.20251057

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Abstract

This work presents new Kneser-type oscillation criteria for second-order quasilinear functional dynamic equations defined on arbitrary unbounded above time scales. Our approach employs the Riccati transformation technique in conjunction with the integral averaging method. The results show a significant improvement over recent Kneser-type oscillation criteria. We provided several illustrative examples to highlight the importance of our findings.

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