Hyers–Ulam stability for a partial difference equation
Under the exponential trichotomy condition we study the Hyers–Ulam stability for the linear partial difference equation: \[ x_{n+1,m}=A_nx_{n,m}+B_{n,m}x_{n,m+1}+f(x_{n,m}),\qquad n,m\in \mathbb{Z} \] where $A_n$ is a $k\times k$ matrix whose elements are sequences of $n$, $B_{n,m}$ is a $k\times...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2021-09-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9350 |
| _version_ | 1797830462641537024 |
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| author | Konstantinos Konstantinidis Garyfalos Papaschinopoulos Christos Schinas |
| author_facet | Konstantinos Konstantinidis Garyfalos Papaschinopoulos Christos Schinas |
| author_sort | Konstantinos Konstantinidis |
| collection | DOAJ |
| description | Under the exponential trichotomy condition we study the Hyers–Ulam stability for the linear partial difference equation:
\[
x_{n+1,m}=A_nx_{n,m}+B_{n,m}x_{n,m+1}+f(x_{n,m}),\qquad n,m\in \mathbb{Z}
\]
where $A_n$ is a $k\times k$ matrix whose elements are sequences of $n$, $B_{n,m}$ is a $k\times k$ matrix whose elements are double sequences of $m,n$ and $f:\mathbb{R}^k\rightarrow \mathbb{R}^k$ is a vector function. We also investigate the Hyers–Ulam stability in the case where the matrices $A_n, B_{n,m}$ and the vector function $f=f_{n,m}$ are constant. |
| first_indexed | 2024-04-09T13:36:27Z |
| format | Article |
| id | doaj.art-bcf86dbc30e44081b8855fc96814d5bb |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:36:27Z |
| publishDate | 2021-09-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-bcf86dbc30e44081b8855fc96814d5bb2023-05-09T07:53:11ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752021-09-0120216711310.14232/ejqtde.2021.1.679350Hyers–Ulam stability for a partial difference equationKonstantinos Konstantinidis0Garyfalos Papaschinopoulos1Christos Schinas2School of Engineering, Democritus University of Thrace, Xanthi, GreeceDemocritus University of Thrace, School of Engineering, Xanthi, Greece School of Engineering, Democritus University of Thrace, Xanthi, 67100, GreeceUnder the exponential trichotomy condition we study the Hyers–Ulam stability for the linear partial difference equation: \[ x_{n+1,m}=A_nx_{n,m}+B_{n,m}x_{n,m+1}+f(x_{n,m}),\qquad n,m\in \mathbb{Z} \] where $A_n$ is a $k\times k$ matrix whose elements are sequences of $n$, $B_{n,m}$ is a $k\times k$ matrix whose elements are double sequences of $m,n$ and $f:\mathbb{R}^k\rightarrow \mathbb{R}^k$ is a vector function. We also investigate the Hyers–Ulam stability in the case where the matrices $A_n, B_{n,m}$ and the vector function $f=f_{n,m}$ are constant.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9350partial difference equationshyers–ulam stabilityexponential trichotomy. |
| spellingShingle | Konstantinos Konstantinidis Garyfalos Papaschinopoulos Christos Schinas Hyers–Ulam stability for a partial difference equation Electronic Journal of Qualitative Theory of Differential Equations partial difference equations hyers–ulam stability exponential trichotomy. |
| title | Hyers–Ulam stability for a partial difference equation |
| title_full | Hyers–Ulam stability for a partial difference equation |
| title_fullStr | Hyers–Ulam stability for a partial difference equation |
| title_full_unstemmed | Hyers–Ulam stability for a partial difference equation |
| title_short | Hyers–Ulam stability for a partial difference equation |
| title_sort | hyers ulam stability for a partial difference equation |
| topic | partial difference equations hyers–ulam stability exponential trichotomy. |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9350 |
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