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Mathematics
Volume 13
Issue 3
10.3390/math13030494
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

On the Oscillation of Fourth-Order Delay Differential Equations via Riccati Transformation

by
Mohamed Mazen
1,*,
Mohamed M. A. El-Sheikh
2,
Samah Euat Tallah
3,* and
Gamal A. F. Ismail
1
1
Department of Mathematics, University College for Women, Ain Shams University, Cairo 11566, Egypt
2
Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Koom 32511, Egypt
3
Basic Science Department, Higher Institute of Management Science & Foreign Trade, Cairo 11765, Egypt
*
Authors to whom correspondence should be addressed.
Mathematics 2025, 13(3), 494; https://doi.org/10.3390/math13030494 (registering DOI)
Submission received: 22 December 2024 / Revised: 27 January 2025 / Accepted: 30 January 2025 / Published: 31 January 2025
Versions Notes

Abstract

This paper deals with the oscillatory behavior of solutions of a general class of fourth-order non-linear delay differential equations. New oscillation criteria are established using Riccati transformation and a Philos-type technique. The obtained results not only improve and extend some published results in the literature, but also relax some traditional conditions on the function ψ(χ(ι)). Three examples are provided to illustrate the main results.
Keywords: delay differential equations; oscillation; Riccati transformation delay differential equations; oscillation; Riccati transformation

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MDPI and ACS Style

Mazen, M.; El-Sheikh, M.M.A.; Euat Tallah, S.; Ismail, G.A.F. On the Oscillation of Fourth-Order Delay Differential Equations via Riccati Transformation. Mathematics 2025, 13, 494. https://doi.org/10.3390/math13030494

AMA Style

Mazen M, El-Sheikh MMA, Euat Tallah S, Ismail GAF. On the Oscillation of Fourth-Order Delay Differential Equations via Riccati Transformation. Mathematics. 2025; 13(3):494. https://doi.org/10.3390/math13030494

Chicago/Turabian Style

Mazen, Mohamed, Mohamed M. A. El-Sheikh, Samah Euat Tallah, and Gamal A. F. Ismail. 2025. "On the Oscillation of Fourth-Order Delay Differential Equations via Riccati Transformation" Mathematics 13, no. 3: 494. https://doi.org/10.3390/math13030494

APA Style

Mazen, M., El-Sheikh, M. M. A., Euat Tallah, S., & Ismail, G. A. F. (2025). On the Oscillation of Fourth-Order Delay Differential Equations via Riccati Transformation. Mathematics, 13(3), 494. https://doi.org/10.3390/math13030494

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