On the Cauchy problem for systems containing locally explicit equations (Q1770182)

Summary: We consider so-called locally explicit equations involving nonlinear differentials. Such equations are characterized by certain continuity and semigroup properties of the corresponding quasiflow and arise typically in the mathematical modelling of nonsmooth mechanical and physical systems. Under some natural hypotheses, we prove the local solvability of the corresponding Cauchy problem by applying Schauder's fixed-point principle to a suitable equivalent integral equation. Afterwards, we illustrate the abstract existence result by means of an application to an automatic regulation system involving a hysteresis element of stop type.