On Two Nonlinear Difference Equations

2015/12/09 by Julius Fergy T. Rabago, Rabago, Julius Fergy T., Jerico B. Bacani +1
Computer Science · Mathematics · Physics and Astronomy · #11B39 #39A10 #Advanced Mathematical Theories and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #math.DS #msc:11B39 #msc:39A10

paper · pdf · doi:10.48550/arxiv.1512.02716

The first version of the paper has been drafted on March 24, 2014

openalex publication_date 2015/12/09 · arxiv created 2015/12/20 · arxiv updated 2015/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The behavior of solutions of the following nonlinear difference equations x_n+1=(q)/(p+x_n^ν) and y_n+1=(q)/(-p+y_n^ν), where p, q ∈ℝ⁺ and ν∈ ℕ are studied. The solution form of these two equations when ν=1 are expressed in terms of Horadam numbers. Furthermore, the behavior of their solutions are investigated for all integer ν> 0 and several numerical examples are presented to illustrate the results exhibited. The present work generalizes those seen in [\it Adv. Differ. Equ., \bf 2013:174 (2013), 7 pages].

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