Rabier, Patrick J.; Rheinboldt, Werner C. A general existence and uniqueness theory for implicit differential- algebraic equations. (English) Zbl 0722.34004 Differ. Integral Equ. 4, No. 3, 563-582 (1991). Existence and uniqueness for solutions of initial value problems involving implicit differential-algebraic equations \(f(t,x,x')=0\) are established under index type conditions. The main result requires the index of the equation to be one, but equations of higher index can also be treated if the derivative of F with respect to \(x'\) has constant rank. Reviewer: T.C.Gard (Athens/Georgia) Cited in 2 ReviewsCited in 25 Documents MSC: 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 34A09 Implicit ordinary differential equations, differential-algebraic equations 34A34 Nonlinear ordinary differential equations and systems 34C40 Ordinary differential equations and systems on manifolds Keywords:Existence and uniqueness; initial value problems; implicit differential- algebraic equations; index type conditions PDFBibTeX XMLCite \textit{P. J. Rabier} and \textit{W. C. Rheinboldt}, Differ. Integral Equ. 4, No. 3, 563--582 (1991; Zbl 0722.34004)