Existence and uniqueness of Carathéodory and Filippov solutions for discontinuous systems of differential equations

We use essential limits inferior and superior of the nonlinear part of a discontinuous ODE to introduce some novel transversality conditions which imply that Filippov solutions are Carathéodory solutions. We also prove some uniqueness criteria based on different Lipschitz conditions on different par...

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Detalles Bibliográficos
Autores: López Pouso, Rodrigo, Rodríguez López, Jorge
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universidad de Santiago de Compostela (USC)
Repositorio:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
Idioma:inglés
OAI Identifier:oai:minerva.usc.gal:10347/44612
Acceso en línea:https://hdl.handle.net/10347/44612
Access Level:acceso abierto
Palabra clave:Discontinuous differential equations
Carathéodory solutions
Filippov solutions
Differential inclusions
Descripción
Sumario:We use essential limits inferior and superior of the nonlinear part of a discontinuous ODE to introduce some novel transversality conditions which imply that Filippov solutions are Carathéodory solutions. We also prove some uniqueness criteria based on different Lipschitz conditions on different parts of the domain separated from one another by boundaries which satisfy certain transversality conditions.