✨
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
🎯
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 $\gamma < \alpha$.
📊
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 $\gamma < \alpha$.
💡
Conclusion & Impact:We provide examples, illustrating the results and state an open problem.
🔬Design:Research Article
📍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.
🔖
Cite This Article
BAZİGHİFAN, 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://ajindex.com/articles/729113