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Dergiler / 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
Sayfa
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Yayın Tarihi
2025-06-01
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The accuracy of the primary findings is demonstrated by examples.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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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Temel Bulgular & Veri: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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Sonuç & Katkı:The accuracy of the primary findings is demonstrated by examples.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (13)

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