LAUSR

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 a 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.