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Journals / Gazi University Journal of Science / 2026 / Volume: 38 Issue: 2

Trichotomy of nonoscillatory solutions for nonlinear first- order neutral difference equation with generalized difference operators

Yaşar Bolat(KASTAMONU ÜNİVERSİTESİ)0000-0002-7978-1078
Murat Gevgeşoğlu(kastamonu üniversitesi)0000-0001-5215-427X
Pages
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Publication Date
2025-06-01
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AI Summary & Key Takeaways

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

The accuracy of the primary findings is demonstrated by examples.

📌 3 Key Takeaways

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Objective & Hypothesis:In this study, we examine the trichotomy of non-oscillatory solution for the nonlinear first-order neutral difference equation ∆_a (x_n-a^(n+1) x_(n-1) )+∆_a (x_(n-1)/b_(n-1) )+q_n f(x_(n-τ) )=0,n∈N_max{1,τ} , where ∆_a x_n=x_(n+1)-ax_n,τ∈N,a∈R^+ with ∆_a^m Δ=∆_a^(m-1) (∆_a ), aⁿ is a general term of exponential sequence, (q_n) is real valued sequences.
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Key Findings & Data:In this study, we examine the trichotomy of non-oscillatory solution for the nonlinear first-order neutral difference equation ∆_a (x_n-a^(n+1) x_(n-1) )+∆_a (x_(n-1)/b_(n-1) )+q_n f(x_(n-τ) )=0,n∈N_max{1,τ} , where ∆_a x_n=x_(n+1)-ax_n,τ∈N,a∈R^+ with ∆_a^m Δ=∆_a^(m-1) (∆_a ), aⁿ is a general term of exponential sequence, (q_n) is real valued sequences.
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Conclusion & Impact:The accuracy of the primary findings is demonstrated by examples.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Trichotomy · Oscillation · Nonoscillation

Abstract

In this study, we examine the trichotomy of non-oscillatory solution for the nonlinear first-order neutral difference equation ∆_a (x_n-a^(n+1) x_(n-1) )+∆_a (x_(n-1)/b_(n-1) )+q_n f(x_(n-τ) )=0,n∈N_max{1,τ} , where ∆_a x_n=x_(n+1)-ax_n,τ∈N,a∈R^+ with ∆_a^m Δ=∆_a^(m-1) (∆_a ), aⁿ is a general term of exponential sequence, (q_n) is real valued sequences. The accuracy of the primary findings is demonstrated by examples.

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Cite This Article

Bolat, Y., Gevgeşoğlu, M. (2025). Trichotomy of nonoscillatory solutions for nonlinear first- order neutral difference equation with generalized difference operators. Gazi University Journal of Science, Volume: 38 Issue: 2. https://doi.org/10.35378/gujs.1383308

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