Authors: Stević, Stevo 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On the recursive sequence xn = 1 + ∑i=1 k αixn-pi/∑j=1 m βjxn-qj
Journal: Discrete Dynamics in Nature and Society
Volume: 2007
Issue: 1
Issue Date: 3-Apr-2007
Rank: M22
ISSN: 1026-0226
DOI: 10.1155/2007/39404
Abstract: 
We give a complete picture regarding the behavior of positive solutions of the following important difference equation: xn = 1 + ∑i=1kαixn-pi/ ∑j=1mβjxn-qj, n ∈ ℕ0, where αi, i ∈ {1,...,k}, and βj, j∈ {1,...,m}, are positive numbers such that ∑i=1k αi = ∑j=1m βj = 1, and pi, i ∈ {1,...,k}, and qj, j ∈ {1,...,m}, are natural numbers such that p1 < p2< ⋯ < pk and q1 < q2 ⋯ < qm. The case when gcd (p1,...,pk,q1,...,qm) = 1 is the most important. For the case we prove that if all pi, i ∈ {1,...,k}, are even and all qj, j ∈ {1,...,m}, are odd, then every positive solution of this equation converges to a periodic solution of period two, otherwise, every positive solution of the equation converges to a unique positive equilibrium.
Publisher: Hindawi

Show full item record

SCOPUSTM   
Citations

21
checked on Nov 24, 2024

Page view(s)

12
checked on Nov 24, 2024

Google ScholarTM

Check

Altmetric

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.