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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This paper concerns quasi-linear implicit differential equations of form 0=A1(x)x'- g1(x), 0=g2(x), where A1:U->L(Rn,Rn-m) is C1, g1:U->Rn-m is C1, g2:U->Rm 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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