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Journals / Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2026 / Cilt: 25 Sayı: 5

Periodic Solutions of Some Higher Order Rational Difference Equations

Bazı Yüksek Mertebeden Rasyonel Fark Denklemlerinin Periyodik Çözümleri

Melih Göcen(ZONGULDAK BÜLENT ECEVİT ÜNİVERSİTESİ)0000-0001-8669-6122
Pages
1091–1094
Publication Date
2025-10-01
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AI Summary & Key Takeaways

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

Moreover, some numerical examples are given to illustrate our theoretical results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, the periodicity of the solutions of some higher order difference equations w_(n+1)=(w_n w_(n-k-1))/w_(n-k) , n, k ∈ N_0 " " are investigated where the initial conditions are arbitrary real numbers such that the denominator is always nonzero.
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Key Findings & Data:While investigating the periodicity of this higher order equation, first the special cases of the equation were considered then a generalization was given for the periodicity of the solution of this higher order difference equation.
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Conclusion & Impact:Moreover, some numerical examples are given to illustrate our theoretical results.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:periyodiklik · fark denklemleri · pozitif çözümler

Abstract

In this paper, the periodicity of the solutions of some higher order difference equations w_(n+1)=(w_n w_(n-k-1))/w_(n-k) , n, k ∈ N_0 " " are investigated where the initial conditions are arbitrary real numbers such that the denominator is always nonzero. While investigating the periodicity of this higher order equation, first the special cases of the equation were considered then a generalization was given for the periodicity of the solution of this higher order difference equation. Moreover, some numerical examples are given to illustrate our theoretical results.

Özet

Bu makalede, başlangıç koşulları paydanın her zaman sıfırdan farklı olacağı şekilde keyfi reel sayılar olmak üzere, bazı yüksek mertebeden w_(n+1)=(w_n w_(n-k-1))/w_(n-k) , n,k ∈ N_0 " " fark denklemlerinin çözümlerinin periyodikliği araştırılmıştır. Bu yüksek mertebeden denklemin periyodikliği araştırılırken önce denklemin özel durumları ele alınmış, daha sonra bu yüksek mertebeden fark denkleminin çözümünün periyodikliği için bir genelleme yapılmıştır. Ayrıca teorik sonuçlarımızı göstermek için bazı sayısal örnekler verilmiştir.

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Cite This Article

Göcen, M. (2025). Periodic Solutions of Some Higher Order Rational Difference Equations. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 25 Sayı: 5, 1091–1094. https://doi.org/10.35414/akufemubid.1569529

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References (14)

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