We establish the robustness of the notion of an exponential dichotomy for a nonautonomous linear delay equation. We consider the general cases of equations satisfying the Carathéodory conditions and of noninvertible evolution families defined by the linear equations. The stable and unstable spaces of the perturbed equations are obtained as images of linear operators that in their turn are fixed points of appropriate contraction maps.

中文翻译：

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时滞方程双曲的鲁棒性

我们建立了非自治线性时滞方程指数二分法概念的鲁棒性。我们考虑满足Carathéodory条件的方程和线性方程定义的不可逆演化族的一般情况。摄动方程的稳定和不稳定空间是作为线性算子的图像获得的，而线性算子又是适当收缩图的固定点。