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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We provide examples, illustrating the results and state an open problem.
📌 3 Key Takeaways
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Objective & Hypothesis:In this work, we obtain necessary and sufficient conditions for the oscillation of all solutions of second-order half-linear delay differential equation of the form $ \bigl(r(y^{\prime})^\gamma\bigr)^{\prime}(t)+ q(t)y^\alpha(\tau(t))=0\,.$ We study this equation under the assumption $\int^{\infty}\big(r(\eta)\big)^{-1/\gamma} d\eta=\infty$ and consider two cases when $\gamma > \alpha$ and $\gamma < \alpha$.
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Key Findings & Data:In this work, we obtain necessary and sufficient conditions for the oscillation of all solutions of second-order half-linear delay differential equation of the form $ \bigl(r(y^{\prime})^\gamma\bigr)^{\prime}(t)+ q(t)y^\alpha(\tau(t))=0\,.$ We study this equation under the assumption $\int^{\infty}\big(r(\eta)\big)^{-1/\gamma} d\eta=\infty$ and consider two cases when $\gamma > \alpha$ and $\gamma < \alpha$.
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Conclusion & Impact:We provide examples, illustrating the results and state an open problem.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Oscillation · nonoscillation · delay
Abstract
In this work, we obtain necessary and sufficient conditions for the oscillation of all solutions of second-order half-linear delay differential equation of the form $ \bigl(r(y^{\prime})^\gamma\bigr)^{\prime}(t)+ q(t)y^\alpha(\tau(t))=0\,.$ We study this equation under the assumption $\int^{\infty}\big(r(\eta)\big)^{-1/\gamma} d\eta=\infty$ and consider two cases when $\gamma > \alpha$ and $\gamma < \alpha$. We provide examples, illustrating the results and state an open problem.
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Cite This Article
Bazighifan, O., Santra, S. S. (2020). Second-order half-linear delay differential equations: Oscillation tests. Advances in the Theory of Nonlinear Analysis and its Application, Cilt: 4 Sayı: 4, 385–393. https://doi.org/10.31197/atnaa.751034