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<p>The aim of this paper is to study the oscillatory behavior of solutions of second-order noncanonical dynamical equations with a sublinear and superlinear neutral terms. Using the process of linearization, we obtain some new easily verifiable criteria for the oscillation of the aforementioned equation. The results are illustrated by three examples. The results are new even for the case <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2024_2795_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {T}}={\mathbb {R}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="double-struck">T</mi> <mo>=</mo> <mi mathvariant="double-struck">R</mi> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2024_2795_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {T}}={\mathbb {Z}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="double-struck">T</mi> <mo>=</mo> <mi mathvariant="double-struck">Z</mi> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Some Novel Conditions for the Oscillation of Second-Order Noncanonical Dynamic Equations with Non-linear Neutral Terms

  • 期刊论文

  • 发表日期：

    2025年1月8日

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  • Said R. Grace,
  • Gokula N. Chhatria

摘要

The aim of this paper is to study the oscillatory behavior of solutions of second-order noncanonical dynamical equations with a sublinear and superlinear neutral terms. Using the process of linearization, we obtain some new easily verifiable criteria for the oscillation of the aforementioned equation. The results are illustrated by three examples. The results are new even for the case \({\mathbb {T}}={\mathbb {R}}\) T = R and \({\mathbb {T}}={\mathbb {Z}}\) T = Z .