ON LINEAR DIFFERENTIAL-ALGEBRAIC EQUATIONS AND LINEARIZATIONS

On the background of a careful analysis of nonlinear DAFs, linearizati ons of nonlinear index-2 systems are considered. Finding appropriate f unction spaces and their topologies allows to apply the standard Impli cit Function Theorem again. Both, solvability statements as well as th e local convergence of the Newton-Kantorovich method (quasilinearizati on) result immediately. In particular, this applies also to fully impl icit index-1 systems whose leading nullspace is allowed to vary with a ll its arguments.