Advancing Oscillation Theory for Neutral Delay Differential Equations
Keywords:
Oscillation Theory, Neutral Differential Equations, Several Deviating Arguments, Mixed Neutral Term.Abstract
In applied mathematics, oscillation is widely recognized, as is its role in fields such as physics, engineering, and medicine. This paper proposes novel criteria for characterizing the oscillatory nature of delay differential equations that contain a mixture of neutral terms. The outcomes of this research expand and simplify existing conditions previously established in the literature. A practical illustration and a numerical analysis are provided as an example to demonstrate the practical significance of the primary findings.
Downloads
References
[1] F. G. Andrade, M. Frasson, and P. Tacuri. Applications to functional differential equations of neutral type. Generalized Ordinary Differential Equations in Abstract Spaces and Applications, 2021:429–453, 2021. 1
[2] R. Arul and V. Shobha. Oscillation of second-order nonlinear neutral differential equations with mixed neutral term. J. Appl. Math. Phys., 3:1080–1089, 2015. 1
[3] G. Chatzarakis, S. Grace, I. Jadlovsk´a, T. Li, and E. Tun ¸c. Oscillation criteria for third-order emden-fowler differential equations with unbounded neutral coefficients. Complexity, 2019(5691758), 2019. 1
4] J. Graef, O. Ozdemir, A. Kaymaz, and E. Tunc. Oscillation of damped second order linear mixed neutral differential equations. Monatshefte f¨ur Mathematik, 194:85–104, 2021. 1
[5] J. Hale. Theory of Functional Differential Equations. Springer: New York, NY, USA, 1977, 1977. 1
[6] T. Li. Comparison theorems for second-order neutral differential equations of mixed type. Electron. J. Differ. Equ., 2010:1–7, 2010. 1
[7] T. Li and Y. Rogovchenko. Oscillation criteria for even-order neutral differential equations. Appl. Math. Lett., 61:35–41, 2019. 1
[8] T. Li and Y. Rogovchenko. On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations. Appl. Math. Lett., 105(106293):1–7, 2020. 1
[9] T. Li, M. Senel, and C. Zhang. Oscillation of solutions to second-order half-linear differential equations with neutral terms. Electron. J. Differ. Equ., 2013:1–7, 2013. 1
[10] E. Thandapani and R. Rama. Comparison and oscillation theorems for second order nonlinear neutral differential equations of mixed type. Serdica Math. J., 39:1–16, 2013. 1
[11] E. Thandapani, S. Selvarangam, M. Vijaya, and R. Rama. Oscillation results for second order nonlinear differential equation with delay and advanced arguments. Kyungpook Math. J., 56:137–146, 2016. 1
[12] C. Zhang, B. Bacul´ıkov´a, J. Dˇzurina, and T. Li. Oscillation results for second order mixed neutral differential equations with distributed deviating arguments. Math. Slovaca, 66:1–12, 2016. 1
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Ali Hasan Ali, Hawraa Almubarak, Zainab H. Ahmed, Firas Ghanim
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
