Rabier, Patrick J.; Rheinboldt, Werner C. A geometric treatment of implicit differential-algebraic equations. (English) Zbl 0804.34004 J. Differ. Equations 109, No. 1, 110-146 (1994). The existence and uniqueness of implicit differential-algebraic equations are proved using a differential-geometric approach to transfer the problem into explicit ordinary differential equations and applying standard theory of ordinary differential equations. The new “geometric treatment” requires weaker rank conditions than what is usually seen. Furthermore an intrinsic index definition of DAEs is presented. Reviewer: C.Bendtsen (Lyngby) Cited in 1 ReviewCited in 62 Documents MSC: 34A09 Implicit ordinary differential equations, differential-algebraic equations 34A26 Geometric methods in ordinary differential equations Keywords:geometric treatment; existence; uniqueness; implicit differential- algebraic equations; differential-geometric approach; intrinsic index definition PDFBibTeX XMLCite \textit{P. J. Rabier} and \textit{W. C. Rheinboldt}, J. Differ. Equations 109, No. 1, 110--146 (1994; Zbl 0804.34004) Full Text: DOI