Differential-algebraic equations and impasse points

Impasse points can occur in the analysis of Differential-Algebraic-Equations (DAE's) that, for example, describe the dynamic behavior of electrical networks. Such points are usually characterized by the condition that solutions of the DAE in question cannot be continued beyond them. However, it turns out that several classes of impasse points, each of which represents different behavior of the DAE, do exist. In this paper, relations between these classes and between impasse points and pseudolimit points are examined for the first time. Sufficient conditions as well as necessary conditions for a point to be an impasse are given. Known results similar to ours are restricted to the class of forward and backward impasse points and concern continuously differentiable solutions only. We extend and generalize them; some become special cases of theorems in this paper. Other results are disproved by our counterexamples.