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Research Article | Open Access

Oscillation criterion for half-linear sublinear functional noncanonical dynamic equations

Taher S. Hassan1,2,3,4( ), Amır AbdelMenaem2, Mouataz Billah Mesmouli1, Wael W. Mohammed1,3, Ismoil Odinaev5, Bassant M. El-Matary6,7
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele Ⅱ, 39, 00186 Roma, Italy
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt
Jadara University Research Center, Jadara University, Jordan
Department of Automated Electrical Systems, Ural Power Engineering Institute, Ural Federal University, 620002 Yekaterinburg, Russia
Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia
Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt
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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.

Keywords

time scalesoscillationhalf-linearsublineardynamic equationsdifferential equations

References

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Electronic Research Archive
Volume 33 Issue 3,
March 2025
Pages 1351-1366
DOI: 10.3934/era.2025062

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Cite this article:
Hassan TS, AbdelMenaem A, Mesmouli MB, et al. Oscillation criterion for half-linear sublinear functional noncanonical dynamic equations. Electronic Research Archive, 2025, 33(3): 1351-1366. https://doi.org/10.3934/era.2025062

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Received: 25 September 2024
Revised: 12 February 2025
Accepted: 28 February 2025
Published: 15 March 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)