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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Under some certain conditions, it is also shown that there exists only one solution.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we prove the well-known Cauchy-Peano theorem for existence of solutions to dynamic equations on time scales.
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Key Findings & Data:Some simple examples are given to show that there may exist more than a single solution for dynamic initial value problems.
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Conclusion & Impact:Under some certain conditions, it is also shown that there exists only one solution.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Cauchy-Peano theorem · Picard-Lidelof theorem · dynamic equations
Abstract
In this paper, we prove the well-known Cauchy-Peano theorem for existence of solutions to dynamic equations on time scales. Some simple examples are given to show that there may exist more than a single solution for dynamic initial value problems. Under some certain conditions, it is also shown that there exists only one solution.
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Cite This Article
KARPUZ, B. (2022). On the existence and uniqueness of solutions to dynamic equations. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 3, 1072–1089. https://ajindex.com/articles/607762