Título:	Stability, asymptotic and exponential stability for various types of equations with discontinuous solutions via Lyapunov functionals
Autor(es):	Gallegos, Claudio Acunã Grau, Rogelio Mesquita, Jaqueline Godoy
ORCID:	https://orcid.org/0000-0002-4630-4101 https://orcid.org/0000-0002-1255-9384
Afiliação do autor:	Universidad de Santiago de Chile, Departamento de Matemática Universidad del Norte, Departamento de Matemáticas y Estadística Universidade de Brasília, Departamento de Matemática
Assunto:	Equação diferencial Integral deHenstock–Kurzweil Teoria de Lyapunov
Data de publicação:	2021
Editora:	Elsevier
Referência:	GALLEGOS,Claudio Acuña, Gallegos, GRAU, Rogelio Grau; MESQUISTA, Jaqueline Godoy. Stability, asymptotic and exponential stability for various types of equations with discontinuous solutions via Lyapunov functionals. Journal of Differential Equations, [S.l.], v. 299. 2021. p. 256-283. DOI:https://doi.org/10.1016/j.jde.2021.07.012. Disponível em: https://www.sciencedirect.com/science/article/pii/S0022039621004496. Acesso em: 12 ago. 2023.
Abstract:	In this paper, we are interested in investigating stability results for generalized ordinary differential equations (generalized ODEs in short), and their applications to measure differential equations and dynamic equations on time scales. First, we establish stability, asymptotic and exponential stability for the trivial solution of generalized ODEs. Secondly, we use the well known correspondence between solutions of generalized ODEs and solutions of measure differential equations, obtaining analogues results for the last equations. Finally, we apply some of these results for dynamic equations on time scales.
Unidade Acadêmica:	Instituto de Ciências Exatas (IE) Departamento de Matemática (IE MAT)
Programa de pós-graduação:	Programa de Pós-Graduação em Matemática
DOI:	https://doi.org/10.1016/j.jde.2021.07.012
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