A Novel Analysis of Oscillatory Properties in Nonlinear Differential Equations With Damping Terms and Advanced Arguments

Azza M. Algatheem, Omar Bazighifan and Fahd Masood

Journal of Mathematics, 2026, vol. 2026, 1-14

Abstract: This research investigates the oscillatory behavior of a class of second-order nonlinear advanced differential equations with a damping term. Sufficient conditions for the oscillation of all solutions were obtained using the Riccati transform and comparison techniques with first-order advanced differential inequalities. The new results are more general and easier to apply than some previous findings, while also easing several of their limitations. Three analytical examples are presented to demonstrate the efficiency of the proposed criteria and their ability to address cases not covered by traditional criteria. This theoretical framework strengthens and supports the development of oscillation studies for advanced differential equations.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:7530956

DOI: 10.1155/jom/7530956

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