Frigon, MarlèneTella Álvarez, MarcosFernández Tojo, Fernando Adrián2021-03-092021-03-092021Frigon, M., Tella, M. & F. Tojo, F.A. First order differential systems with a nonlinear boundary condition via the method of solution-regions. Bound Value Probl 2021, 19 (2021). https://doi.org/10.1186/s13661-021-01495-9http://hdl.handle.net/10347/24677In this article we extend the known theory of solution regions to encompass nonlinear boundary conditions. We both provide results for new boundary conditions and recover some known results for the linear caseeng© The Author(s) 2021. Open Access. 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/Atribución 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/Solution regionsNonlinear boundary conditionsExistence resultsUpper and lower solutionsjournal article10.1186/s13661-021-01495-91687-2770open access