Gunther Reißig and Holger Boche.
A normal form for implicit differential equations near singular points and its application.
Fachtagung Informations- und Mikrosystemtechnik, Magdeburg, Germany, March 25 - 27, 1998, pp. 419-425.

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Full text. (Free access.)

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Abstract:
This paper concerns quasi-linear implicit differential equations of form 0=A₁(x)x'- g₁(x), 0=g₂(x), where A₁:U->L(Rⁿ,R^n-m) is C¹, g₁:U->R^n-m is C¹, g₂:U->R^m is C², U is an open subset of Rⁿ, and m is less than n. In particular, the above differential equation is considered about impasse points x₀ in U, i.e., points x₀ beyond which solutions are not continuable. We review a recent result on a normal form about such points and discuss two examples.

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