Authors: | Hu, Lin Xia Li, Wan Tong Stević, Stevo |
Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts |
Title: | Global asymptotic stability of a second order rational difference equation |
Journal: | Journal of Difference Equations and Applications |
Volume: | 14 |
Issue: | 8 |
First page: | 779 |
Last page: | 797 |
Issue Date: | 1-Aug-2008 |
Rank: | M21 |
ISSN: | 1023-6198 |
DOI: | 10.1080/10236190701827945 |
Abstract: | The main goal of the paper is to confirm Conjecture 9.5.5 stated by Kulenovic and Ladas in Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures (Chapman & Hall/CRC, Boca Raton, FL, 2002). The boundedness, invariant intervals, semicycles and global attractivity of all nonnegative solutions of the equation χn+1 = βχn+γχn-1/A+Bχn+Cχ n-1, n∈ℕ0, are studied, where the parameters β, γ A, B, C ∈ (0, ∞) and the initial conditions χ-1,χ0 ∈ [0, ∞] are such that χ-1 + χ0 > 0. It is shown that if the equation has no prime period-two solutions, then the unique positive equilibrium of the equation is globally asymptotically stable. |
Keywords: | Boundedness | Difference equation | Global attractor | Globally asymptotically stable | Invariant interval | Semicycle |
Publisher: | Taylor & Francis |
Project: | NSFC (No. 10571078) NSF of Gansu Province of China (No. 3ZS061-A25-001) |
Show full item record
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.