On discontinuous differential equations and the method of solution-regions
Jorge Rodr\'iguez-L\'opez
TL;DR
This paper extends the method of solution regions to establish new existence and localization results for discontinuous differential equations, broadening its applicability especially for Carathéodory nonlinearities, supported by illustrative examples.
Contribution
The paper relaxes assumptions on solution regions, enhancing the method's applicability to a wider class of discontinuous differential equations.
Findings
New existence and localization results for discontinuous systems
Broader applicability of the solution regions method
Illustrative examples demonstrating the theory
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 Carath\'eodory nonlinearities. Several examples are provided to illustrate the theory.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Numerical methods for differential equations · Nonlinear Differential Equations Analysis