Existence of Monotone Solutions of a Difference Equation

We consider the nonlinear difference equation xn+1=f(xn−k,xn−k+1,…,xn), n=0,1,…, where k∈{1,2,…} and the initial values x−k,x−k+1,…,x0∈(0,+∞). We give sufficient conditions under which this equation has monotone positive solutions which converge to the equilibrium, extending and including in this...

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Main Authors: Taixiang Sun, Hongjian Xi, Weizhen Quan
Format: Article
Language:English
Published: Wiley 2008-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2008/917560
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author Taixiang Sun
Hongjian Xi
Weizhen Quan
author_facet Taixiang Sun
Hongjian Xi
Weizhen Quan
author_sort Taixiang Sun
collection DOAJ
description We consider the nonlinear difference equation xn+1=f(xn−k,xn−k+1,…,xn), n=0,1,…, where k∈{1,2,…} and the initial values x−k,x−k+1,…,x0∈(0,+∞). 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.
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publishDate 2008-01-01
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series Discrete Dynamics in Nature and Society
spelling doaj-art-cd9daad380f64eeeb33ee2815f4ab81d2025-08-20T03:19:35ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2008-01-01200810.1155/2008/917560917560Existence of Monotone Solutions of a Difference EquationTaixiang Sun0Hongjian Xi1Weizhen Quan2Department of Mathematics, College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, ChinaDepartment of Mathematics, College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, ChinaDepartment of Mathematics, College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, ChinaWe consider the nonlinear difference equation xn+1=f(xn−k,xn−k+1,…,xn), n=0,1,…, where k∈{1,2,…} and the initial values x−k,x−k+1,…,x0∈(0,+∞). 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.http://dx.doi.org/10.1155/2008/917560
spellingShingle Taixiang Sun
Hongjian Xi
Weizhen Quan
Existence of Monotone Solutions of a Difference Equation
Discrete Dynamics in Nature and Society
title Existence of Monotone Solutions of a Difference Equation
title_full Existence of Monotone Solutions of a Difference Equation
title_fullStr Existence of Monotone Solutions of a Difference Equation
title_full_unstemmed Existence of Monotone Solutions of a Difference Equation
title_short Existence of Monotone Solutions of a Difference Equation
title_sort existence of monotone solutions of a difference equation
url http://dx.doi.org/10.1155/2008/917560
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