Gevrey class regularity for analytic differential-delay equations
This paper considers differential-delay equations of the form \[x'(t)=p(t)x(t-1),\] where the coefficient function $p\colon\mathbb{R}\rightarrow\mathbb{C}$ is analytic and not bounded on any $\delta$-neighborhood of the intervals $\left(-\infty,\gamma\right]$, $\gamma\in\mathbb{R}$. For these...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2016-08-01
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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=4247 |
| Summary: | This paper considers differential-delay equations of the form
\[x'(t)=p(t)x(t-1),\]
where the coefficient function $p\colon\mathbb{R}\rightarrow\mathbb{C}$ is analytic and not bounded on any $\delta$-neighborhood of the intervals $\left(-\infty,\gamma\right]$, $\gamma\in\mathbb{R}$. For these equations, we cannot apply the known results regarding the analyticity of the bounded solutions $x\colon (-\infty,\gamma]\rightarrow\mathbb{C}$. We prove Gevrey class regularity for such solutions. |
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| ISSN: | 1417-3875 |