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Unique solutions for a class of discontinuous differential equations. (English) Zbl 0692.34004
Summary: This paper is concerned with the Cauchy problem $$\dot x(t)=f(t,x(t)),$$ $$x(t_ 0)=x_ 0\in {\mathbb{R}}^ n$$, where the vector field f may be discontinuous with respect to both variables t, x. If the total variation of f along certain directions is locally finite, we prove the existence of a unique solution, depending continuously on the initial data.

##### MSC:
 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
##### Keywords:
Carathéodory solution; Cauchy problem
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##### References:
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