Improved Hille-Type and Ohriska-Type Criteria for Half-Linear Third-Order Dynamic Equations

Taher S. Hassan, Mnaouer Kachout, Bassant M. El-Matary (), Loredana Florentina Iambor (), Ismoil Odinaev 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
Mnaouer Kachout: Department of Computer Engineering, College of Computer Science and Engineering, University of Ha’il, Hail 2440, Saudi Arabia
Bassant M. El-Matary: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Loredana Florentina Iambor: Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania
Ismoil Odinaev: Department of Automated Electrical Systems, Ural Power Engineering Institute, Ural Federal University, 620002 Yekaterinburg, Russia
Akbar Ali: Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia

Mathematics, 2024, vol. 12, issue 23, 1-18

Abstract: In this paper, we examine the oscillatory behavior of solutions to a class of half-linear third-order dynamic equations with deviating arguments α 2 ( η ) ϕ δ 2 α 1 η ϕ δ 1 u Δ ( η ) Δ Δ + p ( η ) ϕ δ u ( g ( η ) ) = 0 , on an arbitrary unbounded-above time scale T , where η ∈ [ η 0 , ∞ ) T : = [ η 0 , ∞ ) ∩ T , η 0 ≥ 0 , η 0 ∈ T and ϕ ζ ( w ) : = w ζ sgn w , ζ > 0 . Using the integral mean approach and the known Riccati transform methodology, several improved Hille-type and Ohriska-type oscillation criteria have been derived that do not require some restrictive assumptions in the relevant results. Illustrative examples and conclusions show that these criteria are sharp for all third-order dynamic equations compared to the previous results in the literature.

Keywords: oscillation criteria; Hille-type; Ohriska-type; differential equations; 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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