Existence of Monotone Solutions of a Difference Equation

Taixiang Sun, Hongjian Xi and Weizhen Quan

Discrete Dynamics in Nature and Society, 2008, vol. 2008, 1-8

Abstract:

We consider the nonlinear difference equation 𠑥 𠑛 + 1 = 𠑓 ( 𠑥 𠑛 − 𠑘 , 𠑥 𠑛 − 𠑘 + 1 , … , 𠑥 𠑛 ) , 𠑛 = 0 , 1 , … , where 𠑘 ∈ { 1 , 2 , … } and the initial values 𠑥 − 𠑘 , 𠑥 − 𠑘 + 1 , … , 𠑥 0 ∈ ( 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.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:917560

DOI: 10.1155/2008/917560

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