Existence of monotone solutions of a difference equation
type: Item
instance of: scholarly article
title: Existence of monotone solutions of a difference equation
zbMATH Open document ID: 1160.39309
DOI: 10.1155/2008/917560
author: Taixiang Sun
author: Hongjian Xi
author: Weizhen Quan
published in: Discrete Dynamics in Nature and Society
publication date: 2009-04-01T00:00:00Z
full work available at URL: https://eudml.org/doc/129846
review text: Summary: We consider the nonlinear difference equation \(x_{n+1}=f(x_{n - k},x_{n - k+1},\dots ,x_{n}), n=0,1,\dots ,\) where \(k\in {1,2,\dots }\) and the initial values \(x_{ - k},x_{ - k+1},\dots ,x_{0}\in (0,+\infty )\). We give sufficient conditions under which this equation has monotone positive solutions which converge to the equilibrium, extending and including in this way some results of the literature.
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 5538674
zbMATH Keywords: nonlinear difference equation
zbMATH Keywords: monotone positive solutions
zbMATH Keywords: equilibrium
Wikidata QID: Q58644561
MaRDI profile type: Publication
OpenAlex ID: W2031079390
cites work: A note on positive non-oscillatory solutions of the difference equation
cites work: The difference equation \(x_{n+1}=\alpha + \frac {x_{n-k}}{\Sigma_{i=0}^{k-1} c_{i}x_{n-i}}\) has solutions converging to zero
cites work: On the asymptotics of nonlinear difference equations
cites work: Inclusion Theorems for Non-linear Difference Equations with Applications
cites work: On the Recursive Sequencexn+1=
cites work: Monotonicity of solutions converging to a saddle point equilibrium
cites work: On the behaviour of the solutions of a second-order difference equation
cites work: On the Recursive Sequence
cites work: Convergence of solutions in a nonhyperbolic case.
cites work: Q4664455
cites work: On the recursive sequence \(x_{n+1}=x_{n-1}/g(x_n)\)
cites work: On monotone solutions of some classes of difference equations
cites work: Global stability and asymptotics of some classes of rational difference equations
cites work: On positive solutions of a (\(k+1\))th order difference equation
cites work: Asymptotics of some classes of higher-order difference equations
cites work: Existence of nontrivial solutions of a rational difference equation
cites work: On the solutions of a class of difference equations
cites work: Short Note: On non-oscillatory solutions of the recursive sequence
cites work: On convergence of a recursive sequence \(x_{n+1}= f(x_{n-1},x_n)\)
cites work: Existence of monotone solutions of some difference equations with unstable equilibrium
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description: scientific article; zbMATH DE number 5538674