New iterative criteria for testing the oscillation of solutions of differential equations with distributed deviating arguments

Adeebah Alofee; Ahmed S. Almohaimeed; Osama Moaaz; Adeebah Alofee; Ahmed S. Almohaimeed; Osama Moaaz

doi:10.3934/era.2025155

Electronic Research Archive

2025, Volume 33, Issue 6: 3496-3516. doi: 10.3934/era.2025155

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Research article

New iterative criteria for testing the oscillation of solutions of differential equations with distributed deviating arguments

Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia

Received: 15 February 2025 Revised: 18 April 2025 Accepted: 09 May 2025 Published: 09 June 2025

The objective of this work was to provide sufficient conditions for testing the oscillatory performance of solutions of the neutral second-order differential equation with distributed deviation arguments. We derived improved relations that influence the oscillation parameters of the equation under study. We used comparison with lower-order equations and Riccati techniques to derive the oscillation parameters. Comparing our findings with earlier pertinent findings allows us to assess the advancements made in oscillation theory. Furthermore, some numerical solutions for a special case of the equation under study are presented, and the numerical and theoretical results are compared.
- differential equation,
- second-order equations,
- neutral argument,
- oscillatory behavior,
- equations with distributed deviating arguments
Citation: Adeebah Alofee, Ahmed S. Almohaimeed, Osama Moaaz. New iterative criteria for testing the oscillation of solutions of differential equations with distributed deviating arguments[J]. Electronic Research Archive, 2025, 33(6): 3496-3516. doi: 10.3934/era.2025155

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Abstract

The objective of this work was to provide sufficient conditions for testing the oscillatory performance of solutions of the neutral second-order differential equation with distributed deviation arguments. We derived improved relations that influence the oscillation parameters of the equation under study. We used comparison with lower-order equations and Riccati techniques to derive the oscillation parameters. Comparing our findings with earlier pertinent findings allows us to assess the advancements made in oscillation theory. Furthermore, some numerical solutions for a special case of the equation under study are presented, and the numerical and theoretical results are compared.

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