Note on difference equations with the right-hand side function nonincreasing in each variable

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2022-02-23
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Springer Nature
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Abstract
We present an example of a difference equation of arbitrary order, possessing the right-hand side function that is homogeneous to a certain degree and nonincreasing in each variable, which has a unique positive equilibrium, as well as solutions that do not converge to the equilibrium. The example shows that the main result in the paper: O. Moaaz, Dynamics of difference equation x(n+1) = f (x(n-l), x(n-k)) (Adv. Differ. Equ. 2018:447, 2018), is incorrect.
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Difference equationUnbounded solutionsNondecreasing functionHomogeneous function
Citation
Journal of Inequalities and Applications. 2022, vol. 2022, issue 1, p. 1-7.
https://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/s13660-022-02761-9
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Peer-reviewed
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en
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Creative Commons Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
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10.1186/s13660-022-02761-9
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http://hdl.handle.net/11012/203957
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