Bazı Yüksek Mertebeden Rasyonel Fark Denklemlerinin Periyodik Çözümleri

Year 2025, Volume: 25 Issue: 5, 1091 - 1094, 01.10.2025

Melih Göcen

https://doi.org/10.35414/akufemubid.1569529

Abstract

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.

Keywords

periyodiklik , fark denklemleri , pozitif çözümler , p-döngüsü

Periodic Solutions of Some Higher Order Rational Difference Equations

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.

Keywords

Periodicity , difference equations , positive solutions , p-cycle

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