Abstract
This paper concerns differential equation systems on $\mathbb R^n$ with discontinuous right--hand sides. We deal with non-smooth vector fields in $\mathbb R^n$ having a codimension-one submanifold $M$ as its discontinuity set. After a regularization of a such system and a global blow-up we are able to bring out some results that bridge the space between discontinuous systems and singularly perturbed smooth systems.
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