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Unique solutions for a class of discontinuous differential equations


Author: Alberto Bressan
Journal: Proc. Amer. Math. Soc. 104 (1988), 772-778
MSC: Primary 34A10; Secondary 34A60
MathSciNet review: 964856
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Abstract: This paper is concerned with the Cauchy Problem

$\displaystyle \dot x\left( t \right) = f\left( {t,x\left( t \right)} \right),\quad x\left( {{t_0}} \right) = {x_0} \in {\mathbb{R}^n},$

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.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0964856-0
Article copyright: © Copyright 1988 American Mathematical Society