A new class of generalized ordinary differential equations with applications

Abstract

The space of parametric b-measures endowed with appropriate topologies is introduced to define a new class of generalized ODEs given by parametric b-measures. This framework offers a new approach for dealing with precompact families of Carath\'eodory ODEs using nonautonomous dynamical systems techniques. An application to the study of the dynamics of the fast variables of a slow-fast system of ODEs, where the fast motion is determined by a Carath\'eodory vector field with equicontinuous $m$-bounds and bounded $l$-bounds, is given.