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 |
| Summary: | 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. |
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| ISSN: | 1417-3875 |