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