Unique solutions for a class of discontinuous differential equations
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- by Alberto Bressan PDF
- Proc. Amer. Math. Soc. 104 (1988), 772-778 Request permission
Abstract:
This paper is concerned with the Cauchy Problem \[ \dot x\left ( t \right ) = f\left ( {t,x\left ( t \right )} \right ),\quad x\left ( {{t_0}} \right ) = {x_0} \in {\mathbb {R}^n},\] 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.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 772-778
- MSC: Primary 34A10; Secondary 34A60
- DOI: https://doi.org/10.1090/S0002-9939-1988-0964856-0
- MathSciNet review: 964856