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.

Full text.
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**Abstract:**

This paper concerns quasi-linear implicit
differential equations of form
0=A_{1}(x)x'- g_{1}(x), 0=g_{2}(x),
where
A_{1}:U->L(R^{n},R^{n-m}) is C^{1},
g_{1}:U->R^{n-m} is C^{1},
g_{2}:U->R^{m} is C^{2},
U is an open subset of R^{n},
and m is less than n.
In particular, the above differential equation
is considered about
impasse points x_{0} in U, i.e., points x_{0} 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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