Singular initial value problems for scalar quasi-linear ordinary differential equations

We discuss existence, non-uniqueness and regularity of one- two-sided solutions initial value problems for scalar quasi-linear ordinary differential equations where the condition corresponds to an impasse point equation. With a geometric approach, we reduce problem questions in dynamical systems theory. As application, detail second-order form g(x)u?=f(x,u,u?) with imposed at simple zero g. This generalises results by Liang also makes them more transparent via our approach.