Note on difference equations with the right-hand side function nonincreasing in each variable
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 e...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-02-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-022-02761-9 |
| _version_ | 1823962410144235520 |
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| author | Stevo Stević Bratislav Iričanin Witold Kosmala Zdeněk Šmarda |
| author_facet | Stevo Stević Bratislav Iričanin Witold Kosmala Zdeněk Šmarda |
| author_sort | Stevo Stević |
| collection | DOAJ |
| description | 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 ) $x_{n+1}=f(x_{n-l}, x_{n-k})$ (Adv. Differ. Equ. 2018:447, 2018), is incorrect. |
| first_indexed | 2024-12-17T17:17:11Z |
| format | Article |
| id | doaj.art-929a8e5045974f31b120d04ae255b745 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-17T17:17:11Z |
| publishDate | 2022-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-929a8e5045974f31b120d04ae255b7452022-12-21T21:39:55ZengSpringerOpenJournal of Inequalities and Applications1029-242X2022-02-01202211710.1186/s13660-022-02761-9Note on difference equations with the right-hand side function nonincreasing in each variableStevo Stević0Bratislav Iričanin1Witold Kosmala2Zdeněk Šmarda3Mathematical Institute of the Serbian Academy of SciencesFaculty of Electrical Engineering, University of BelgradeDepartment of Mathematical Sciences, Appalachian State UniversityDepartment of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of TechnologyAbstract 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 ) $x_{n+1}=f(x_{n-l}, x_{n-k})$ (Adv. Differ. Equ. 2018:447, 2018), is incorrect.https://doi.org/10.1186/s13660-022-02761-9Difference equationUnbounded solutionsNondecreasing functionHomogeneous function |
| spellingShingle | Stevo Stević Bratislav Iričanin Witold Kosmala Zdeněk Šmarda Note on difference equations with the right-hand side function nonincreasing in each variable Journal of Inequalities and Applications Difference equation Unbounded solutions Nondecreasing function Homogeneous function |
| title | Note on difference equations with the right-hand side function nonincreasing in each variable |
| title_full | Note on difference equations with the right-hand side function nonincreasing in each variable |
| title_fullStr | Note on difference equations with the right-hand side function nonincreasing in each variable |
| title_full_unstemmed | Note on difference equations with the right-hand side function nonincreasing in each variable |
| title_short | Note on difference equations with the right-hand side function nonincreasing in each variable |
| title_sort | note on difference equations with the right hand side function nonincreasing in each variable |
| topic | Difference equation Unbounded solutions Nondecreasing function Homogeneous function |
| url | https://doi.org/10.1186/s13660-022-02761-9 |
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