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Research Article | Open Access

Oscillation criterion of Kneser type for half-linear second-order dynamic equations with deviating arguments

Taher S. Hassan1,2,3( ), Amir Abdel Menaem4, Yousef Jawarneh1, Naveed Iqbal1, Akbar Ali1
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, Roma 00186, Italy
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Department of Automated Electrical Systems, Ural Power Engineering Institute, Ural Federal University, 620002 Yekaterinburg, Russia
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Abstract

This paper employed the well-known Riccati transformation method to deduce a Kneser-type oscillation criterion for second-order dynamic equations. These results are considered an extension and improvement of the known Kneser results for second-order differential equations and are new for other time scales. We have included examples to highlight the significance of the results we achieved.

Keywords

Kneser-typeoscillationsecond-orderhalf-lineardynamic equationtime scales
CLC number: 39A10, 39A99, 34N05, 34K11

References

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AIMS Mathematics
Volume 9 Issue 7,
July 2024
Pages 19446-19458
DOI: 10.3934/math.2024947

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Hassan TS, Menaem AA, Jawarneh Y, et al. Oscillation criterion of Kneser type for half-linear second-order dynamic equations with deviating arguments. AIMS Mathematics, 2024, 9(7): 19446-19458. https://doi.org/10.3934/math.2024947

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Received: 18 April 2024
Revised: 28 May 2024
Accepted: 05 June 2024
Published: 15 July 2024
©2024 the Author(s), licensee AIMS Press.

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