Opuscula Math. 43, no. 3 (2023), 455-467

Opuscula Mathematica

New oscillation constraints for even-order delay differential equations

Osama Moaaz
Mona Anis
Ahmed A. El-Deeb
Ahmed M. Elshenhab

Abstract. The purpose of this paper is to study the oscillatory properties of solutions to a class of delay differential equations of even order. We focus on criteria that exclude decreasing positive solutions. As in this paper, this type of solution emerges when considering the noncanonical case of even equations. By finding a better estimate of the ratio between the Kneser solution with and without delay, we obtain new constraints that ensure that all solutions to the considered equation oscillate. The new findings improve some previous findings in the literature.

Keywords: delay differential equations, even-order, Kneser solutions, oscillation.

Mathematics Subject Classification: 34C10, 34K11.

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  • Osama Moaaz (corresponding author)
  • ORCID iD https://orcid.org/0000-0003-3850-1022
  • Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
  • Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt
  • Communicated by Josef Diblík.
  • Received: 2022-06-01.
  • Revised: 2023-03-04.
  • Accepted: 2023-03-04.
  • Published online: 2023-05-17.
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Cite this article as:
Osama Moaaz, Mona Anis, Ahmed A. El-Deeb, Ahmed M. Elshenhab, New oscillation constraints for even-order delay differential equations, Opuscula Math. 43, no. 3 (2023), 455-467, https://doi.org/10.7494/OpMath.2023.43.3.455

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