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Journals / Hacettepe Journal of Mathematics and Statistics / 2023 / Cilt: 52 - Sayı: 2

Asymptotic equivalence of impulsive dynamic equations on time scales

Sibel DOĞRU AKGÖL
Pages
277–291
Publication Date
2023-03-31
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Some illustrative examples are also provided, including an application to a generalized Duffing equation.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The asymptotic equivalence of linear and quasilinear impulsive dynamic equations on time scales, as well as two types of linear equations, are proven under mild conditions.
📊
Key Findings & Data:To establish the asymptotic equivalence of two impulsive dynamic equations a method has been developed that does not require restrictive conditions, such as the boundedness of the solutions.
💡
Conclusion & Impact:Some illustrative examples are also provided, including an application to a generalized Duffing equation.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:asymptotic equivalence · dynamic equations · time scales

Abstract

The asymptotic equivalence of linear and quasilinear impulsive dynamic equations on time scales, as well as two types of linear equations, are proven under mild conditions. To establish the asymptotic equivalence of two impulsive dynamic equations a method has been developed that does not require restrictive conditions, such as the boundedness of the solutions. Not only the time scale extensions of former results have been obtained, but also improved for impulsive differential equations defined on the real line. Some illustrative examples are also provided, including an application to a generalized Duffing equation.

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Cite This Article

AKGÖL, S. D. (2023). Asymptotic equivalence of impulsive dynamic equations on time scales. Hacettepe Journal of Mathematics and Statistics, Cilt: 52 - Sayı: 2, 277–291. https://ajindex.com/articles/886279

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