Regularization and singular perturbation techniques for non-smooth systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

This paper is concerned with some aspects of the qualitative-geometric theory of non-smooth systems. We present a survey of the state of the art on the connection between the regularization process of nonsmooth vector fields and the singular perturbation problems. As a matter of fact, the main results in our setting fill a gap between these areas. Exploiting such results, applications to constrained differential equations are discussed. (C) 2011 Elsevier B.V. All rights reserved.