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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In this work we establish some new sufficient conditions for oscillation of fourth-order nonlinear neutral delay dynamic equations of the form $(\alpha(t)([x(t)-p(t)x(h(t))]^{\triangle\triangle\triangle})^{\alpha})^{\triangle}+q(t)x^{\beta}(g(t))=0$ , $t\epsilon[t_{0},\infty)_{T}$ where α and β are quotients of positive odd integers with β ≤ α.
📌 3 Key Takeaways
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Objective & Hypothesis:In this work we establish some new sufficient conditions for oscillation of fourth-order nonlinear neutral delay dynamic equations of the form $(\alpha(t)([x(t)-p(t)x(h(t))]^{\triangle\triangle\triangle})^{\alpha})^{\triangle}+q(t)x^{\beta}(g(t))=0$ , $t\epsilon[t_{0},\infty)_{T}$ where α and β are quotients of positive odd integers with β ≤ α.
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Key Findings & Data:In this work we establish some new sufficient conditions for oscillation of fourth-order nonlinear neutral delay dynamic equations of the form $(\alpha(t)([x(t)-p(t)x(h(t))]^{\triangle\triangle\triangle})^{\alpha})^{\triangle}+q(t)x^{\beta}(g(t))=0$ , $t\epsilon[t_{0},\infty)_{T}$ where α and β are quotients of positive odd integers with β ≤ α.
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Conclusion & Impact:In this work we establish some new sufficient conditions for oscillation of fourth-order nonlinear neutral delay dynamic equations of the form $(\alpha(t)([x(t)-p(t)x(h(t))]^{\triangle\triangle\triangle})^{\alpha})^{\triangle}+q(t)x^{\beta}(g(t))=0$ , $t\epsilon[t_{0},\infty)_{T}$ where α and β are quotients of positive odd integers with β ≤ α.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Oscillation · Neutral · Time scales
Abstract
In this work we establish some new sufficient conditions for oscillation of fourth-order nonlinear neutral delay dynamic equations of the form $(\alpha(t)([x(t)-p(t)x(h(t))]^{\triangle\triangle\triangle})^{\alpha})^{\triangle}+q(t)x^{\beta}(g(t))=0$ , $t\epsilon[t_{0},\infty)_{T}$ where α and β are quotients of positive odd integers with β ≤ α.
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Cite This Article
ZAFER, A., GRACE, S. R. (2022). Oscillation of fourth-order nonlinear neutral delay dynamic equations. Hacettepe Journal of Mathematics and Statistics, Cilt: 44 - Sayı: 2, 331–339. https://ajindex.com/articles/530238