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<p>This study aims to analyze the oscillatory behavior of solutions of higher-order functional differential equations in the compulsory nonlinear case. The study identifies certain asymptotic features of positive solutions of this type of equation, taking into account the noncanonical situation. Based on these asymptotic features, we establish a multi-conditional criterion to guarantee the oscillation, which is an extension of the previous second-order results. Additionally, we develop a new simplified criterion not provided in previous nonlinear case studies to address the multiplicity of constraints in the first criterion. Finally, we illustrate the effectiveness of the simplified criterion by applying the results to two examples.</p>

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Oscillatory Performance of Solutions to Even-Order Delay Differential Equations with Compulsory Nonlinearity

  • 期刊论文

  • 发表日期：

    2025年10月18日

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  • Osama Moaaz,
  • Wedad Albalawi,
  • Refah M. Alotaibi

摘要

This study aims to analyze the oscillatory behavior of solutions of higher-order functional differential equations in the compulsory nonlinear case. The study identifies certain asymptotic features of positive solutions of this type of equation, taking into account the noncanonical situation. Based on these asymptotic features, we establish a multi-conditional criterion to guarantee the oscillation, which is an extension of the previous second-order results. Additionally, we develop a new simplified criterion not provided in previous nonlinear case studies to address the multiplicity of constraints in the first criterion. Finally, we illustrate the effectiveness of the simplified criterion by applying the results to two examples.