Higher order averaging theory for finding periodic solutions via Brouwer degree

In this paper we deal with nonlinear differential systems of the form x'(t) = Xki=0εiFi(t, x) + εk+1R(t, x, ε), where Fi : R × D → Rn for i = 0, 1, · · · , k, and R : R × D × (-ε0, ε0) → Rn are continuous functions, T-periodic in the first variable, being D an open subset of Rn, and ε a small p...

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Detalhes bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Novaes, Douglas D.|||0000-0002-9147-8442, Teixeira, Marco Antonio|||0000-0002-5386-9282
Formato: artículo
Fecha de publicación:2014
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150723
Acesso em linha:https://ddd.uab.cat/record/150723
https://dx.doi.org/urn:doi:10.1088/0951-7715/27/3/563
Access Level:acceso abierto
Palavra-chave:Averaging theory
Brower degree
Periodic solutions
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spelling Higher order averaging theory for finding periodic solutions via Brouwer degreeLlibre, Jaume|||0000-0002-9511-5999Novaes, Douglas D.|||0000-0002-9147-8442Teixeira, Marco Antonio|||0000-0002-5386-9282Averaging theoryBrower degreePeriodic solutionsIn this paper we deal with nonlinear differential systems of the form x'(t) = Xki=0εiFi(t, x) + εk+1R(t, x, ε), where Fi : R × D → Rn for i = 0, 1, · · · , k, and R : R × D × (-ε0, ε0) → Rn are continuous functions, T-periodic in the first variable, being D an open subset of Rn, and ε a small parameter. For such differential systems, which do not need to be of class C1, under convenient assumptions we extend the averaging theory for computing their periodic solutions to k-th order in ε. Some applications are also performed. 22014-01-0120142014-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/150723https://dx.doi.org/urn:doi:10.1088/0951-7715/27/3/563reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-03437Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2009/SGR-410European Commission https://doi.org/10.13039/501100000780 318999European Commission https://doi.org/10.13039/501100000780 316338open accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:1507232026-06-06T12:50:31Z
dc.title.none.fl_str_mv Higher order averaging theory for finding periodic solutions via Brouwer degree
title Higher order averaging theory for finding periodic solutions via Brouwer degree
spellingShingle Higher order averaging theory for finding periodic solutions via Brouwer degree
Llibre, Jaume|||0000-0002-9511-5999
Averaging theory
Brower degree
Periodic solutions
title_short Higher order averaging theory for finding periodic solutions via Brouwer degree
title_full Higher order averaging theory for finding periodic solutions via Brouwer degree
title_fullStr Higher order averaging theory for finding periodic solutions via Brouwer degree
title_full_unstemmed Higher order averaging theory for finding periodic solutions via Brouwer degree
title_sort Higher order averaging theory for finding periodic solutions via Brouwer degree
dc.creator.none.fl_str_mv Llibre, Jaume|||0000-0002-9511-5999
Novaes, Douglas D.|||0000-0002-9147-8442
Teixeira, Marco Antonio|||0000-0002-5386-9282
author Llibre, Jaume|||0000-0002-9511-5999
author_facet Llibre, Jaume|||0000-0002-9511-5999
Novaes, Douglas D.|||0000-0002-9147-8442
Teixeira, Marco Antonio|||0000-0002-5386-9282
author_role author
author2 Novaes, Douglas D.|||0000-0002-9147-8442
Teixeira, Marco Antonio|||0000-0002-5386-9282
author2_role author
author
dc.subject.none.fl_str_mv Averaging theory
Brower degree
Periodic solutions
topic Averaging theory
Brower degree
Periodic solutions
description In this paper we deal with nonlinear differential systems of the form x'(t) = Xki=0εiFi(t, x) + εk+1R(t, x, ε), where Fi : R × D → Rn for i = 0, 1, · · · , k, and R : R × D × (-ε0, ε0) → Rn are continuous functions, T-periodic in the first variable, being D an open subset of Rn, and ε a small parameter. For such differential systems, which do not need to be of class C1, under convenient assumptions we extend the averaging theory for computing their periodic solutions to k-th order in ε. Some applications are also performed.
publishDate 2014
dc.date.none.fl_str_mv 2
2014-01-01
2014
2014-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/150723
https://dx.doi.org/urn:doi:10.1088/0951-7715/27/3/563
url https://ddd.uab.cat/record/150723
https://dx.doi.org/urn:doi:10.1088/0951-7715/27/3/563
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-03437
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2009/SGR-410
European Commission https://doi.org/10.13039/501100000780 318999
European Commission https://doi.org/10.13039/501100000780 316338
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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