Periodic solutions of measure functional differential equations
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.jde.2021.11.031 http://hdl.handle.net/11449/222949 |
Resumo: | In this article, we study the existence of periodic solutions for measure functional differential equations of the form x(t)=x(0)+∫0tf(s,xs)ds+∫0tg(s,xs)du(s), defined for every t∈R, under suitable assumptions on f,g and u, where the integrals on the right–hand side exist in the Perron and Perron–Stieltjes sense, respectively. We make use of a topological transversality theorem to obtain the main result. Some examples are presented to illustrate the developed theory. Moreover, we apply the results obtained in the context of measure functional differential equations to establish the existence of periodic solutions for a class of impulsive functional differential equations. |
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Periodic solutions of measure functional differential equationsImpulsive differential equationsMeasure functional differential equationsPeriodic solutionsTopological transversalityIn this article, we study the existence of periodic solutions for measure functional differential equations of the form x(t)=x(0)+∫0tf(s,xs)ds+∫0tg(s,xs)du(s), defined for every t∈R, under suitable assumptions on f,g and u, where the integrals on the right–hand side exist in the Perron and Perron–Stieltjes sense, respectively. We make use of a topological transversality theorem to obtain the main result. Some examples are presented to illustrate the developed theory. Moreover, we apply the results obtained in the context of measure functional differential equations to establish the existence of periodic solutions for a class of impulsive functional differential equations.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Universidade Estadual Paulista (UNESP) Instituto de Geociências e Ciências Exatas, Câmpus de Rio Claro, Avenida 24-A, 1515, Bela VistaInstituto de Ciências Matemáticas e de Computação Universidade de São Paulo-Campus de São Carlos, Caixa Postal 668Universidade Estadual Paulista (UNESP) Instituto de Geociências e Ciências Exatas, Câmpus de Rio Claro, Avenida 24-A, 1515, Bela VistaFAPESP: 2019/03188-7CNPq: 310540/2019-4CAPES: PROEX-10537140/DUniversidade Estadual Paulista (UNESP)Universidade de São Paulo (USP)Afonso, S. M. [UNESP]Bonotto, E. M.da Silva, Márcia R.2022-04-28T19:47:44Z2022-04-28T19:47:44Z2022-02-05info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article196-230http://dx.doi.org/10.1016/j.jde.2021.11.031Journal of Differential Equations, v. 309, p. 196-230.1090-27320022-0396http://hdl.handle.net/11449/22294910.1016/j.jde.2021.11.0312-s2.0-85120182326Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Differential Equations21719info:eu-repo/semantics/openAccess2023-05-18T18:21:08Zoai:repositorio.unesp.br:11449/222949Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T18:44:47.653483Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Periodic solutions of measure functional differential equations |
title |
Periodic solutions of measure functional differential equations |
spellingShingle |
Periodic solutions of measure functional differential equations Afonso, S. M. [UNESP] Impulsive differential equations Measure functional differential equations Periodic solutions Topological transversality |
title_short |
Periodic solutions of measure functional differential equations |
title_full |
Periodic solutions of measure functional differential equations |
title_fullStr |
Periodic solutions of measure functional differential equations |
title_full_unstemmed |
Periodic solutions of measure functional differential equations |
title_sort |
Periodic solutions of measure functional differential equations |
author |
Afonso, S. M. [UNESP] |
author_facet |
Afonso, S. M. [UNESP] Bonotto, E. M. da Silva, Márcia R. |
author_role |
author |
author2 |
Bonotto, E. M. da Silva, Márcia R. |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (UNESP) Universidade de São Paulo (USP) |
dc.contributor.author.fl_str_mv |
Afonso, S. M. [UNESP] Bonotto, E. M. da Silva, Márcia R. |
dc.subject.por.fl_str_mv |
Impulsive differential equations Measure functional differential equations Periodic solutions Topological transversality |
topic |
Impulsive differential equations Measure functional differential equations Periodic solutions Topological transversality |
description |
In this article, we study the existence of periodic solutions for measure functional differential equations of the form x(t)=x(0)+∫0tf(s,xs)ds+∫0tg(s,xs)du(s), defined for every t∈R, under suitable assumptions on f,g and u, where the integrals on the right–hand side exist in the Perron and Perron–Stieltjes sense, respectively. We make use of a topological transversality theorem to obtain the main result. Some examples are presented to illustrate the developed theory. Moreover, we apply the results obtained in the context of measure functional differential equations to establish the existence of periodic solutions for a class of impulsive functional differential equations. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-04-28T19:47:44Z 2022-04-28T19:47:44Z 2022-02-05 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1016/j.jde.2021.11.031 Journal of Differential Equations, v. 309, p. 196-230. 1090-2732 0022-0396 http://hdl.handle.net/11449/222949 10.1016/j.jde.2021.11.031 2-s2.0-85120182326 |
url |
http://dx.doi.org/10.1016/j.jde.2021.11.031 http://hdl.handle.net/11449/222949 |
identifier_str_mv |
Journal of Differential Equations, v. 309, p. 196-230. 1090-2732 0022-0396 10.1016/j.jde.2021.11.031 2-s2.0-85120182326 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Journal of Differential Equations 21719 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
196-230 |
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_ |
1808128973311311872 |