Exponential Ordering for Neutral Functional Differential Equations With Non-Autonomous Linear D-Operator
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916111233056768 |
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| author | Obaya, Rafael Villarragut, Víctor M. |
| author_facet | Obaya, Rafael Villarragut, Víctor M. |
| contents | We study neutral functional differential equations with stable linear non-autonomous $D$-operator. The operator of convolution $\hat{D}$ transforms $BU$ into $BU$. We show that, if $D$ is stable, then $\hat{D}$ is invertible and, besides, $\hat{D}$ and $\hat{D}^{-1}$ are uniformly continuous for the compact-open topology on bounded sets. We introduce a new transformed exponential order and, under convenient assumptions, we deduce the 1-covering property of minimal sets. These conclusions are applied to describe the amount of material in a class of compartmental systems extensively studied in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17918 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exponential Ordering for Neutral Functional Differential Equations With Non-Autonomous Linear D-Operator Obaya, Rafael Villarragut, Víctor M. Dynamical Systems 37B55, 34K40, 34K14 We study neutral functional differential equations with stable linear non-autonomous $D$-operator. The operator of convolution $\hat{D}$ transforms $BU$ into $BU$. We show that, if $D$ is stable, then $\hat{D}$ is invertible and, besides, $\hat{D}$ and $\hat{D}^{-1}$ are uniformly continuous for the compact-open topology on bounded sets. We introduce a new transformed exponential order and, under convenient assumptions, we deduce the 1-covering property of minimal sets. These conclusions are applied to describe the amount of material in a class of compartmental systems extensively studied in the literature. |
| title | Exponential Ordering for Neutral Functional Differential Equations With Non-Autonomous Linear D-Operator |
| topic | Dynamical Systems 37B55, 34K40, 34K14 |
| url | https://arxiv.org/abs/2401.17918 |