Oscillation criterion for half-linear sublinear functional noncanonical dynamic equations

Taher S. Hassan; Amır AbdelMenaem; Mouataz Billah Mesmouli; Wael W. Mohammed; Ismoil Odinaev; Bassant M. El-Matary; Taher S. Hassan; Amır AbdelMenaem; Mouataz Billah Mesmouli; Wael W. Mohammed; Ismoil Odinaev; Bassant M. El-Matary

doi:10.3934/era.2025062

Electronic Research Archive

2025, Volume 33, Issue 3: 1351-1366. doi: 10.3934/era.2025062

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Research article

Oscillation criterion for half-linear sublinear functional noncanonical dynamic equations

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele Ⅱ, 39, 00186 Roma, Italy
3.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt
4.
Jadara University Research Center, Jadara University, Jordan
5.
Department of Automated Electrical Systems, Ural Power Engineering Institute, Ural Federal University, 620002 Yekaterinburg, Russia
6.
Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia
7.
Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt

Received: 25 September 2024 Revised: 12 February 2025 Accepted: 28 February 2025 Published: 07 March 2025

In this study, we derive new criteria that ensure the oscillation of solutions to noncanonical dynamic equations that are half-linear sublinear functional. These results not only resolve an open issue in numerous works in the literature but also emulate Ohriskatype and Hille-type criteria for canonical dynamic equations. We provide examples to demonstrate the accuracy, usefulness, and flexibility of the main results.
- time scales,
- oscillation,
- half-linear,
- sublinear,
- dynamic equations,
- differential equations
Citation: Taher S. Hassan, Amır AbdelMenaem, Mouataz Billah Mesmouli, Wael W. Mohammed, Ismoil Odinaev, Bassant M. El-Matary. Oscillation criterion for half-linear sublinear functional noncanonical dynamic equations[J]. Electronic Research Archive, 2025, 33(3): 1351-1366. doi: 10.3934/era.2025062

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Abstract

In this study, we derive new criteria that ensure the oscillation of solutions to noncanonical dynamic equations that are half-linear sublinear functional. These results not only resolve an open issue in numerous works in the literature but also emulate Ohriskatype and Hille-type criteria for canonical dynamic equations. We provide examples to demonstrate the accuracy, usefulness, and flexibility of the main results.

References

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