We illustrate the improvement over the known results by applying and comparing our method with the other known methods on the particular example of Euler-type equations.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we study the second-order half-linear delay differential equation of the form\[(r(t)(y'(t))^\alpha)'+q(t)y^\alpha(\tau(t))= 0.\:\:\:(E)\]We establish new oscillation criteria for (E), which improve a number of related ones in the literature.
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Key Findings & Data:Our approach essentially involves establishing sharper estimates for the positive solutions of (E) than those presented in known works and a comparison principle with first-order delay differential inequalities.
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Conclusion & Impact:We illustrate the improvement over the known results by applying and comparing our method with the other known methods on the particular example of Euler-type equations.
In this paper, we study the second-order half-linear delay differential equation of the form\[(r(t)(y'(t))^\alpha)'+q(t)y^\alpha(\tau(t))= 0.\:\:\:(E)\]We establish new oscillation criteria for (E), which improve a number of related ones in the literature. Our approach essentially involves establishing sharper estimates for the positive solutions of (E) than those presented in known works and a comparison principle with first-order delay differential inequalities. We illustrate the improvement over the known results by applying and comparing our method with the other known methods on the particular example of Euler-type equations.
CHATZARAKİS, G. E., JADLOVSKA, İ. (2019). Improved oscillation results for second-order half-linear delay differential equations. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 1, 170–179. https://ajindex.com/articles/669403
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