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arXiv · 1912.10735

A note on an expansion formula with application to nonlinear DAE's

Matthias Stiefenhofer
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Abstract

In [DL] systems of differential polynomials are investigated with respect to properties of Artin approximation type. The key tool in [DL] is an extended version of a formula by Hurwitz [Hu] expressing high order derivatives of an expansion by lower ones. The formula is further refined in [VFZ] to deliver sufficient conditions concerning the existence of power series solutions of scalar algebraic differential equations of order n. In the paper at hand, the main results from [VFZ] are first reproduced and further extended to systems of nonlinear differential algebraic equations. In addition, a simple extension of Tougeron's implicit function theorem is given in a specific constellation. The results follow from [S1], [S2] where Artin approximation is treated within a Banach space setting, thereby constructing an expansion formula that expresses accurately the required dependency of low and high order derivatives within the system of undetermined coefficients.

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Matthias Stiefenhofer. 2019-12-23. A note on an expansion formula with application to nonlinear DAE's. https://arxiv.org/abs/1912.10735

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