Boundedness of solutions

Detalhes bibliográficos
Autor(a) principal: Afonso, Suzete M. [UNESP]
Data de Publicação: 2021
Outros Autores: Da Silva, Fernanda Andrade, Bonotto, Everaldo M., Federson, Márcia, Grau, Rogelio, Mesquita, Jaqueline G., Toon, Eduard
Tipo de documento: Capítulo de livro
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1002/9781119655022.ch11
http://hdl.handle.net/11449/230094
Resumo: This chapter presents the concepts of uniform boundedness, quasiuniform boundedness, and uniform ultimate boundedness in the scenery of generalized ordinary differential equations (ODEs). It includes criteria of uniform boundedness and uniform ultimate boundedness for the generalized ODE. The chapter presents some results concerning the boundedness of solutions for the generalized ODE using Lyapunov functionals. The correspondence between the solutions of the generalized ODE and the solutions of the measure differential equation (MDE) allows us to conclude that the MDE is also uniformly bounded. By using the results and the correspondence between generalized ODEs and MDEs, the chapter presents the results on boundedness for MDEs. It concludes by showing the extension of one of these results to a certain impulsive differential equation.
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spelling Boundedness of solutionsLyapunov functionalMeasure differential equationOrdinary differential equationsQuasiuniform boundednessUniform boundednessUniform ultimate boundednessThis chapter presents the concepts of uniform boundedness, quasiuniform boundedness, and uniform ultimate boundedness in the scenery of generalized ordinary differential equations (ODEs). It includes criteria of uniform boundedness and uniform ultimate boundedness for the generalized ODE. The chapter presents some results concerning the boundedness of solutions for the generalized ODE using Lyapunov functionals. The correspondence between the solutions of the generalized ODE and the solutions of the measure differential equation (MDE) allows us to conclude that the MDE is also uniformly bounded. By using the results and the correspondence between generalized ODEs and MDEs, the chapter presents the results on boundedness for MDEs. It concludes by showing the extension of one of these results to a certain impulsive differential equation.Departamento de Matemática Instituto de Geociências e Ciências Exatas Universidade Estadual Paulista “Júlio de Mesquita Filho” (UNESP)Departamento de Matemática Instituto de Ciências Matemáticas e de Computação (ICMC) Universidade de São PauloDepartamento de Matemática Aplicada e Estatística Instituto de Ciências Matemáticas e de Computação (ICMC) Universidade de São PauloDepartamento de Matemáticas y Estadística División de Ciencias Básicas Universidad del NorteDepartamento de Matemática Instituto de Ciências Exatas Universidade de BrasíliaDepartamento de Matemática Instituto de Ciências Exatas Universidade Federal de Juiz de ForaDepartamento de Matemática Instituto de Geociências e Ciências Exatas Universidade Estadual Paulista “Júlio de Mesquita Filho” (UNESP)Universidade Estadual Paulista (UNESP)Universidade de São Paulo (USP)Universidad del NorteUniversidade de Brasília (UnB)Universidade Federal de Juiz de ForaAfonso, Suzete M. [UNESP]Da Silva, Fernanda AndradeBonotto, Everaldo M.Federson, MárciaGrau, RogelioMesquita, Jaqueline G.Toon, Eduard2022-04-29T08:37:46Z2022-04-29T08:37:46Z2021-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/bookPart341-359http://dx.doi.org/10.1002/9781119655022.ch11Generalized Ordinary Differential Equations in Abstract Spaces and Applications, p. 341-359.http://hdl.handle.net/11449/23009410.1002/9781119655022.ch112-s2.0-85121529556Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengGeneralized Ordinary Differential Equations in Abstract Spaces and Applicationsinfo:eu-repo/semantics/openAccess2022-04-29T08:37:46Zoai:repositorio.unesp.br:11449/230094Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462022-04-29T08:37:46Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Boundedness of solutions
title Boundedness of solutions
spellingShingle Boundedness of solutions
Afonso, Suzete M. [UNESP]
Lyapunov functional
Measure differential equation
Ordinary differential equations
Quasiuniform boundedness
Uniform boundedness
Uniform ultimate boundedness
title_short Boundedness of solutions
title_full Boundedness of solutions
title_fullStr Boundedness of solutions
title_full_unstemmed Boundedness of solutions
title_sort Boundedness of solutions
author Afonso, Suzete M. [UNESP]
author_facet Afonso, Suzete M. [UNESP]
Da Silva, Fernanda Andrade
Bonotto, Everaldo M.
Federson, Márcia
Grau, Rogelio
Mesquita, Jaqueline G.
Toon, Eduard
author_role author
author2 Da Silva, Fernanda Andrade
Bonotto, Everaldo M.
Federson, Márcia
Grau, Rogelio
Mesquita, Jaqueline G.
Toon, Eduard
author2_role author
author
author
author
author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
Universidade de São Paulo (USP)
Universidad del Norte
Universidade de Brasília (UnB)
Universidade Federal de Juiz de Fora
dc.contributor.author.fl_str_mv Afonso, Suzete M. [UNESP]
Da Silva, Fernanda Andrade
Bonotto, Everaldo M.
Federson, Márcia
Grau, Rogelio
Mesquita, Jaqueline G.
Toon, Eduard
dc.subject.por.fl_str_mv Lyapunov functional
Measure differential equation
Ordinary differential equations
Quasiuniform boundedness
Uniform boundedness
Uniform ultimate boundedness
topic Lyapunov functional
Measure differential equation
Ordinary differential equations
Quasiuniform boundedness
Uniform boundedness
Uniform ultimate boundedness
description This chapter presents the concepts of uniform boundedness, quasiuniform boundedness, and uniform ultimate boundedness in the scenery of generalized ordinary differential equations (ODEs). It includes criteria of uniform boundedness and uniform ultimate boundedness for the generalized ODE. The chapter presents some results concerning the boundedness of solutions for the generalized ODE using Lyapunov functionals. The correspondence between the solutions of the generalized ODE and the solutions of the measure differential equation (MDE) allows us to conclude that the MDE is also uniformly bounded. By using the results and the correspondence between generalized ODEs and MDEs, the chapter presents the results on boundedness for MDEs. It concludes by showing the extension of one of these results to a certain impulsive differential equation.
publishDate 2021
dc.date.none.fl_str_mv 2021-01-01
2022-04-29T08:37:46Z
2022-04-29T08:37:46Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/bookPart
format bookPart
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1002/9781119655022.ch11
Generalized Ordinary Differential Equations in Abstract Spaces and Applications, p. 341-359.
http://hdl.handle.net/11449/230094
10.1002/9781119655022.ch11
2-s2.0-85121529556
url http://dx.doi.org/10.1002/9781119655022.ch11
http://hdl.handle.net/11449/230094
identifier_str_mv Generalized Ordinary Differential Equations in Abstract Spaces and Applications, p. 341-359.
10.1002/9781119655022.ch11
2-s2.0-85121529556
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Generalized Ordinary Differential Equations in Abstract Spaces and Applications
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 341-359
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1799965667851501568

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