Authors: Stević, Stevo 
Iričanin, Bratislav
Kosmala, Witold
Šmarda, Zdeněk
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Note on difference equations with the right-hand side function nonincreasing in each variable
Journal: Journal of Inequalities and Applications
Volume: 1
First page: 25
Issue Date: 1-Jan-2022
Rank: ~M21a
ISSN: 1025-5834
DOI: 10.1186/s13660-022-02761-9
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 xn+1= f(xn−l, xn−k) (Adv. Differ. Equ. 2018:447, 2018), is incorrect.
Keywords: Difference equation | Homogeneous function | Nondecreasing function | Unbounded solutions
Publisher: Springer Link

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