Beyond Peano's theorem: a variational look at discontinuous ODE systems

Abstract

We propose a framework to define solutions of ODE systems under a novel condition that goes well beyond the usual continuity condition required in the classical theory of ODEs (Peano's or Picard's theorems). We illustrate our results with some simple but enlightening examples, including some facts about Sobolev fields, and mention some relevant questions to proceed with this analysis further.