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arXiv · 2205.00960

On the solution manifold of a differential equation with a delay which has a zero

Hans-Otto Walther
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Abstract

For a differential equation with a state-dependent delay we show that the associated solution manifold $X_f$ of codimnsion 1 in the space $C^1([-r,0],\mathbb {R})$ is an almost graph over a hyperplane, which implies that $X_f$ is diffeomorphic to the hyperplane. For the case considered previous results only provide a covering by 2 almost graphs.

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Hans-Otto Walther. 2022-05-02. On the solution manifold of a differential equation with a delay which has a zero. https://arxiv.org/abs/2205.00960

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