Rodríguez López, Jorge2025-11-242025-11-242025-06-23Rodríguez-López, J. (2026). On discontinuous differential equations and the method of solution regions. Journal of Mathematical Analysis and Applications, 553(1), 129827. 10.1016/j.jmaa.2025.1298270022-247Xhttps://hdl.handle.net/10347/43984We adapt the method of solution regions to prove new existence and localization results for systems of discontinuous differential equations. Some assumptions concerning the definition of a solution region are relaxed and thus our results enlarge the applicability of this method even in the case of Carathéodory nonlinearities. Several examples are provided to illustrate the theory.eng© 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Discontinuous differential equationsSolution regionsUpper and lower solutions12 Matemáticasjournal article10.1016/j.jmaa.2025.129827open access