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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
When the delay term τ (t) is not necessarily monotone, we present a new sufficient condition for the oscillation of first-order delay dynamic equations on time scales.
📌 3 Key Takeaways
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Objective & Hypothesis:In this work, we consider the first-order dynamic equations x ∆(t) + p(t)x (τ (t)) = 0, t ∈ [t0, ∞)T where p ∈ Crd ( [t0, ∞)T, R + ) , τ ∈ Crd ([t0, ∞)T, T) and τ (t) ≤ t, limt→∞ τ (t) = ∞.
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Key Findings & Data:In this work, we consider the first-order dynamic equations x ∆(t) + p(t)x (τ (t)) = 0, t ∈ [t0, ∞)T where p ∈ Crd ( [t0, ∞)T, R + ) , τ ∈ Crd ([t0, ∞)T, T) and τ (t) ≤ t, limt→∞ τ (t) = ∞.
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Conclusion & Impact:When the delay term τ (t) is not necessarily monotone, we present a new sufficient condition for the oscillation of first-order delay dynamic equations on time scales.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
In this work, we consider the first-order dynamic equations x ∆(t) + p(t)x (τ (t)) = 0, t ∈ [t0, ∞)T where p ∈ Crd ( [t0, ∞)T, R + ) , τ ∈ Crd ([t0, ∞)T, T) and τ (t) ≤ t, limt→∞ τ (t) = ∞. When the delay term τ (t) is not necessarily monotone, we present a new sufficient condition for the oscillation of first-order delay dynamic equations on time scales.
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Cite This Article
ÖCALAN, Ö. (2022). An improved oscillation criteria for first order dynamic equations. Turkish Journal of Mathematics, Cilt: 45 - Sayı: 1, 487–495. https://ajindex.com/articles/607409