New and improved oscillation criteria for second-order noncanonical neutral differential equations with distributed deviating arguments

Ercan Tunç

doi:10.15672/hujms.1649721

New and improved oscillation criteria for second-order noncanonical neutral differential equations with distributed deviating arguments

Abstract

\begin{abstract} This paper addresses the oscillatory behavior of second-order noncanonical neutral differential equation with distributed deviating arguments of the form \[ \left[r(t)\left(\left(x(t)+p(t)x(\tau(t))\right)^{\prime}\right)^{\alpha}\right]^{\prime} + \int_{b_{1}}^{b_{2}}q(t,v)x^{\beta}(\sigma(t,v))dv=0 \] with \[ \int_{t_{0}}^{\infty} \frac{1}{r^{1/\alpha}(t)} dt<\infty. \] Based on the approaches in the literature, the oscillation of the equation considered is established by means of a single condition. The criteria presented here are new, and they improve and extend some known ones appearing in the literature and also significantly simplify the oscillation analysis of solutions to equations of this type. A few examples are given to illustrate the applicability of all the results obtained. \end{abstract}

Keywords

Thanks

Acknowledgements This article is dedicated to the memory of my mother, Günaydın Tunç (1938-2021).

References

1] R.P. Agarwal, C. Zhang and T. Li, Some remarks on oscillation of second order neutral differential equations, Appl. Math. Comput. 274, 178–181, 2016.

Details

Primary Language

English

Subjects

Ordinary Differential Equations, Difference Equations and Dynamical Systems

Journal Section

Research Article

Authors

Ercan Tunç ^*
Türkiye

Early Pub Date

December 30, 2025

Publication Date

December 30, 2025

Submission Date

March 2, 2025

Acceptance Date

November 26, 2025

Published in Issue

Year 2026 Number: Advanced Online Publication

DOI

https://doi.org/10.15672/hujms.1649721

IZ

https://izlik.org/JA95NA72XZ

Cite

RIS / Bibtex

APA

Tunç, E. (2025). New and improved oscillation criteria for second-order noncanonical neutral differential equations with distributed deviating arguments. Hacettepe Journal of Mathematics and Statistics, Advanced Online Publication. https://doi.org/10.15672/hujms.1649721

AMA

1.Tunç E. New and improved oscillation criteria for second-order noncanonical neutral differential equations with distributed deviating arguments. Hacettepe Journal of Mathematics and Statistics. 2025;(Advanced Online Publication). doi:10.15672/hujms.1649721

Chicago

Tunç, Ercan. 2025. “New and Improved Oscillation Criteria for Second-Order Noncanonical Neutral Differential Equations With Distributed Deviating Arguments”. Hacettepe Journal of Mathematics and Statistics, no. Advanced Online Publication. https://doi.org/10.15672/hujms.1649721.

EndNote

Tunç E (December 1, 2025) New and improved oscillation criteria for second-order noncanonical neutral differential equations with distributed deviating arguments. Hacettepe Journal of Mathematics and Statistics Advanced Online Publication

IEEE

[1]E. Tunç, “New and improved oscillation criteria for second-order noncanonical neutral differential equations with distributed deviating arguments”, Hacettepe Journal of Mathematics and Statistics, no. Advanced Online Publication, Dec. 2025, doi: 10.15672/hujms.1649721.

ISNAD

Tunç, Ercan. “New and Improved Oscillation Criteria for Second-Order Noncanonical Neutral Differential Equations With Distributed Deviating Arguments”. Hacettepe Journal of Mathematics and Statistics. Advanced Online Publication (December 1, 2025). https://doi.org/10.15672/hujms.1649721.

JAMA

1.Tunç E. New and improved oscillation criteria for second-order noncanonical neutral differential equations with distributed deviating arguments. Hacettepe Journal of Mathematics and Statistics. 2025. doi:10.15672/hujms.1649721.

MLA

Tunç, Ercan. “New and Improved Oscillation Criteria for Second-Order Noncanonical Neutral Differential Equations With Distributed Deviating Arguments”. Hacettepe Journal of Mathematics and Statistics, no. Advanced Online Publication, Dec. 2025, doi:10.15672/hujms.1649721.

Vancouver

1.Ercan Tunç. New and improved oscillation criteria for second-order noncanonical neutral differential equations with distributed deviating arguments. Hacettepe Journal of Mathematics and Statistics. 2025 Dec. 1;(Advanced Online Publication). doi:10.15672/hujms.1649721