| Abstract: |
| In this talk, we present a new class of generalized ordinary differential equations. Our motivation arises from the fact that solutions of limiting equations associated with certain Carath\`{e}odory ODEs may lose the property of absolute continuity, while remaining continuous and of bounded variation on compact intervals. Several approaches can be employed to address these irregular limiting equations. We propose a novel method, based on the introduction of a class of generalized ODEs given by parametric b-measures, aimed at preserving the aforementioned properties of solutions for the equations in the hull, as well as ensuring the compactness of the hull. This framework allows us to apply techniques from nonautonomous dynamical systems to the study of precompact families of Carath\`{e}odory ODEs. |
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