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

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  • Azza M. Algatheem
  • Omar Bazighifan
  • Fahd Masood

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.

Suggested Citation

  • Azza M. Algatheem & Omar Bazighifan & Fahd Masood, 2026. "A Novel Analysis of Oscillatory Properties in Nonlinear Differential Equations With Damping Terms and Advanced Arguments," Journal of Mathematics, Hindawi, vol. 2026, pages 1-14, September.
    • Handle: RePEc:hin:jjmath:7530956
    DOI: 10.1155/jom/7530956
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