A note for ``On the rational recursive sequence \(x_{n+1}=\frac{A+\sum^k_{i=0} \alpha_i x_{n-i}}{\sum^k_{i=0} \beta_ix_{n-i}}\)

DOI10.1016/j.ajmsc.2011.05.001zbMath1320.39015OpenAlexW2325425568MaRDI QIDQ763040

Xianyi Li, Li Zhou

Publication date: 8 March 2012

Published in: Arab Journal of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ajmsc.2011.05.001

zbMATH Keywords

global asymptotic stabilityboundedness and persistencerational difference equationinclusion theoremexistence of non-oscillatory solution

Mathematics Subject Classification ID

Growth, boundedness, comparison of solutions to difference equations (39A22) Oscillation theory for difference equations (39A21)

Related Items (1)

Dichotomy between a generalized Lyness difference equation with period-two coefficients and its perturbation

Cites Work

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• Global asymptotic stability in a rational recursive sequence
• Global attractivity in the recursive sequence \(x_{n+1}=(\alpha-\beta x_{n})/(\gamma-x_{n-1})\)
• On the recursive sequences \(x_{n+1}=\frac {-\alpha x_{n-1}}{\beta\pm x_n}\)
• Two rational recursive sequences
• On the recursive sequence \(x_{n+1}=\alpha + x_{n-1}/x_n\)
• Global behavior for a fourth-order rational difference equation
• On the rational recursive sequence $ \ x_{n+1}=\Big ( A+\sum _{i=0}^k\alpha _ix_{n-i}\Big ) \Big / \sum _{i=0}^k\beta _ix_{n-i} $
• Open problems and conjectures
• Inclusion Theorems for Non-linear Difference Equations with Applications
• Asymptotic stability for difference equations with decreasing arguments
• THE RULE OF TRAJECTORY STRUCTURE AND GLOBAL ASYMPTOTIC STABILITY FOR A FOURTH-ORDER RATIONAL DIFFERENCE EQUATION

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