On discontinuous differential equations and the method of solution regions

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2025_journal_rodriguez_discontinuous.pdf (598.41 KB)
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URI: https://hdl.handle.net/10347/43984
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2025.129827

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2025-06-23

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Elsevier
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Abstract

We 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.

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Discontinuous differential equations| Solution regions| Upper and lower solutions

Bibliographic citation

Rodríguez-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.2025.129827

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The author was partially supported by Xunta de Galicia (Spain), project ED431C 2019/02 and AEI, Spain and FEDER, grant PID2020-113275GB-I00.

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© 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/).
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Estatística, Análise Matemática e Optimización