Stieltjes differential systems with non monotonic derivators

Abstract: In this work we study Stieltjes differential systems of which the derivators are allowed to change sign. This leads to the definition of the notion of \emph{function of controlled variation}, a characterization of precompact sets of $g$-continuous functions, and an explicit expression of $g$-exponential maps. Finally, we prove a Peano-type existence result and apply it to a model of fluid stratification on buoyant miscible jets and plumes.