Frigon, MarlèneFernández Tojo, Fernando Adrián2020-04-272020-04-272020Frigon, M., Tojo, F.A.F. Stieltjes differential systems with nonmonotonic derivators. Bound Value Probl 2020, 41 (2020). https://doi.org/10.1186/s13661-020-01345-0http://hdl.handle.net/10347/21786In 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.eng© The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/Stieltjes derivativesDifferential systemsFundamental Theorem of CalculusAscoli–Arzelà TheoremFluid stratificationjournal article10.1186/s13661-020-01345-01687-2770open access