Hyers-Ulam stability and exponential dichotomy of linear differential periodic systems are equivalent
Let $m$ be a positive integer and $q$ be a positive real number. We prove that the $m$-dimensional and $q$-periodic system \begin{equation}\tag{$\ast$} \dot x(t)=A(t)x(t),\qquad t\in\mathbb{R}_+, \qquad x(t)\in\mathbb{C}^m \end{equation} is Hyers-Ulam stable if and only if the monodromy matrix asso...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2015-09-01
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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=3918 |
| Summary: | Let $m$ be a positive integer and $q$ be a positive real number. We prove that the $m$-dimensional and $q$-periodic system
\begin{equation}\tag{$\ast$}
\dot x(t)=A(t)x(t),\qquad t\in\mathbb{R}_+, \qquad x(t)\in\mathbb{C}^m
\end{equation}
is Hyers-Ulam stable if and only if the monodromy matrix associated to the family $\{A(t)\}_{t\ge 0}$ posses a discrete dichotomy, i.e. its spectrum does not intersect the unit circle. |
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| ISSN: | 1417-3875 1417-3875 |