On discontinuous differential equations and the method of solution-regions

2023/02/12 by Jorge Rodríguez López, Rodríguez-López, Jorge
Mathematics · #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2302.05821

openalex publication_date 2023/02/12 · openalex created_date 2023/02/15 · openalex updated_date 2026/08/01

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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