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||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 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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