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Zeitschrift für Analysis und ihre Anwendungen

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Volume 23, Issue 4, 2004, pp. 819–824
DOI: 10.4171/ZAA/1225

Published online: 2004-12-31

On the Cauchy Problem for Systems Containing Locally Explicit Equations

Irina N. Pryadko[1]

(1) University of Voronezh, Russian Federation

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 non-smooth 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.

Keywords: Locally explicit equation, Cauchy problem, quasiflow, semigroup property, local solvability, hysteresis nonlinearity, non-smooth mechanical system

Pryadko Irina: On the Cauchy Problem for Systems Containing Locally Explicit Equations. Z. Anal. Anwend. 23 (2004), 819-824. doi: 10.4171/ZAA/1225