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arXiv · 2401.17918

Exponential Ordering for Neutral Functional Differential Equations With Non-Autonomous Linear D-Operator

Rafael Obaya·Víctor M. Villarragut
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Abstract

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.

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Rafael Obaya, Víctor M. Villarragut. 2024-01-31. Exponential Ordering for Neutral Functional Differential Equations With Non-Autonomous Linear D-Operator. https://doi.org/10.1007/s10884-011-9210-9

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