New Oscillation Results for Second-Order Advanced Differential Equations with Mixed Neutral Nonlinearities
- 1Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
- 2Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Abstract
This paper investigates the oscillatory behavior of a new class of second-order nonlinear neutral advanced differential equations with mixed superlinear and sublinear neutral terms in the noncanonical case. The coexistence of these nonlinearities substantially increases the analytical complexity and limits the applicability of many existing oscillation criteria. To address this challenge, a new analytical framework is developed by establishing qualitative properties of eventually positive solutions. Based on this framework, new oscillation criteria are derived by combining the comparison method with the generalized Riccati transformation. The proposed results provide a unified treatment of the cases m>n, m=n, and m<n. Several explicit criteria are further obtained as direct consequences through suitable choices of auxiliary functions. Illustrative examples demonstrate the applicability and effectiveness of the theoretical results. Overall, the proposed framework broadens the scope of existing oscillation theory and provides a unified approach for this class of nonlinear advanced neutral differential equations in the noncanonical case.
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BibTeX
@article{alqahtani2026oscillation,
title = {{New Oscillation Results for Second-Order Advanced Differential Equations with Mixed Neutral Nonlinearities}},
author = {Zuhur Alqahtani and Belgees Qaraad and Areej Almuneef and Fahd Masood},
journal = {Axioms},
year = {2026},
month = oct,
doi = {10.3390/axioms15100774},
url = {https://www.mdpi.com/2075-1680/15/10/774},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - New Oscillation Results for Second-Order Advanced Differential Equations with Mixed Neutral Nonlinearities
AU - Zuhur Alqahtani
AU - Belgees Qaraad
AU - Areej Almuneef
AU - Fahd Masood
PY - 2026
DA - 2026/10/16
JO - Axioms
DO - 10.3390/axioms15100774
UR - https://www.mdpi.com/2075-1680/15/10/774
AB - This paper investigates the oscillatory behavior of a new class of second-order nonlinear neutral advanced differential equations with mixed superlinear and sublinear neutral terms in the noncanonical case. The coexistence of these nonlinearities substantially increases the analytical complexity and limits the applicability of many existing oscillation criteria. To address this challenge, a new analytical framework is developed by establishing qualitative properties of eventually positive solutions. Based on this framework, new oscillation criteria are derived by combining the comparison method with the generalized Riccati transformation. The proposed results provide a unified treatment of the cases m>n, m=n, and m<n. Several explicit criteria are further obtained as direct consequences through suitable choices of auxiliary functions. Illustrative examples demonstrate the applicability and effectiveness of the theoretical results. Overall, the proposed framework broadens the scope of existing oscillation theory and provides a unified approach for this class of nonlinear advanced neutral differential equations in the noncanonical case.
SN - 2075-1680
ER -