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arXiv · 2304.06838

Exponential dichotomy for a class of asymptotically autonomous delayed differential equations

Heli Elorreaga·Adrian Gomez
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Abstract

In this work we give a criterion to have an exponential dichotomy over all $\mathbb{R}$ for delayed systems $x'(t)=L(t)x_t$, where $L_{\pm}=\lim_{t\to\pm\infty}L(t)$, and the systems $x'(t)=L_{\pm}x_t$ are autonomous and hyperbolic. The proof is based in a suitable choice of weighted Sobolev spaces $L^p(\mathbb{R},\mu)$ and $W^{1,p}(\mathbb{R},\mu)$, where the involves differential operators become Fredholm's operators and this property are strongly exploited.

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Heli Elorreaga, Adrian Gomez. 2023-04-13. Exponential dichotomy for a class of asymptotically autonomous delayed differential equations. https://arxiv.org/abs/2304.06838

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