New Oscillation Criteria for Sturm–Liouville Dynamic Equations with Deviating Arguments

Taher S. Hassan (), Clemente Cesarano, Loredana Florentina Iambor (), Amir Abdel Menaem, Naveed Iqbal 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
Clemente Cesarano: Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
Loredana Florentina Iambor: Department of Mathematics and Computer Science, University of Oradea, Univeritatii nr.1, 410087 Oradea, Romania
Amir Abdel Menaem: Department of Automated Electrical Systems, Ural Power Engineering Institute, Ural Federal University, 620002 Yekaterinburg, Russia
Naveed Iqbal: Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Akbar Ali: Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia

Mathematics, 2024, vol. 12, issue 10, 1-11

Abstract: The aim of this study is to refine the known Riccati transformation technique to provide new oscillation criteria for solutions to second-order dynamic equations over time. It is important to note that the convergence or divergence of some improper integrals on time scales depends not only on the integration function but also on the integration time scale. Therefore, there has been a motivation to find new oscillation criteria that can be applicable regardless of whether ∫ ζ 0 ∞ Δ ξ a ( ξ ) is convergent or divergent, in contrast to what has been followed in most previous works in the literature. We have provided an example to illustrate the significance of the obtained results.

Keywords: oscillation behavior; second-order; linear; dynamic equations; time scales (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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