Enhanced Oscillation Criteria of Solutions for Half-Linear Dynamic Equations on Arbitrary Time Scales

Taher S. Hassan (), Loredana Florentina Iambor (), Mouataz Billah Mesmouli, Eltigani I. Hassan, Khaled Aldwoah and Akbar Ali
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Taher S. Hassan: Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Loredana Florentina Iambor: Department of Mathematics and Computer Science, University of Oradea, Univeritatii nr. 1, 410087 Oradea, Romania
Mouataz Billah Mesmouli: Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Eltigani I. Hassan: Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia
Khaled Aldwoah: Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia
Akbar Ali: Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia

Mathematics, 2025, vol. 13, issue 17, 1-17

Abstract: This paper presents some oscillation criteria for second-order half-linear dynamic equations defined on unbounded above arbitrary time scales. These criteria offer sufficient conditions for all solutions of the equations to display oscillatory behavior. We investigate both delay and advanced cases of these equations, and our approach encompasses a broader class of dynamic equations than previously considered in the literature. The results of this study not only generalize well-known oscillation criteria used in differential equations but also significantly broaden their applicability to arbitrary time scales. Additionally, we provide illustrative examples to demonstrate the relevance and accuracy of our findings.

Keywords: oscillation; second order; half-linear; dynamic equations; time scales (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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