Improved Kneser-type oscillation criterion for half-linear dynamic equations on time scales

Taher S. Hassan; Amir Abdel Menaem; Hasan Nihal Zaidi; Khalid Alenzi; Bassant M. El-Matary; Taher S. Hassan; Amir Abdel Menaem; Hasan Nihal Zaidi; Khalid Alenzi; Bassant M. El-Matary

doi:10.3934/math.20241426

AIMS Mathematics

2024, Volume 9, Issue 10: 29425-29438. doi: 10.3934/math.20241426

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Improved Kneser-type oscillation criterion for half-linear dynamic equations on time scales

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
Department of Automated Electrical Systems, Ural Power Engineering Institute, Ural Federal University, 620002 Yekaterinburg, Russia
3.
Electrical Engineering Department, Mansoura University, Mansoura 35516, Egypt
4.
Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia

Received: 31 August 2024 Revised: 29 September 2024 Accepted: 08 October 2024 Published: 17 October 2024
MSC : 39A10, 39A21, 39A99, 34C10, 34C15, 34K11, 34K42, 34N05

We study the Kneser-type oscillation criterion for a class of second-order half-linear functional dynamic equations on an arbitrary time scale utilizing the integral averaging approach and the Riccati transformation method. The results show an improvement in Kneser-type when compared to some known results. We provide some illustrative examples to demonstrate the significance of our main results.
- oscillation criteria,
- Kneser-type,
- half-linear,
- dynamic equation,
- time scales,
- differential equations
Citation: Taher S. Hassan, Amir Abdel Menaem, Hasan Nihal Zaidi, Khalid Alenzi, Bassant M. El-Matary. Improved Kneser-type oscillation criterion for half-linear dynamic equations on time scales[J]. AIMS Mathematics, 2024, 9(10): 29425-29438. doi: 10.3934/math.20241426

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Abstract

We study the Kneser-type oscillation criterion for a class of second-order half-linear functional dynamic equations on an arbitrary time scale utilizing the integral averaging approach and the Riccati transformation method. The results show an improvement in Kneser-type when compared to some known results. We provide some illustrative examples to demonstrate the significance of our main results.

References

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