Existence of at most two limit cycles for some non-autonomous differential equations

It is know that the non-autonomous differential equations dx/dt = a(t) + b(t)|x|, where a(t) and b(t) are 1-periodic maps of class C1, have no upper bound for their number of limit cycles (isolated solutions satisfying x(0) = x(1)). We prove that if either a(t) or b(t) does not change sign, then the...

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Autores: Gasull, Armengol|||0000-0002-1719-8231, Zhao, Yulin|||0000-0002-4179-2409
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:275381
Acceso en línea:https://ddd.uab.cat/record/275381
https://dx.doi.org/urn:doi:10.3934/cpaa.2023016
Access Level:acceso abierto
Palabra clave:Non-autonomous differential equation
Limit cycle
Periodic orbit
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spelling Existence of at most two limit cycles for some non-autonomous differential equationsGasull, Armengol|||0000-0002-1719-8231Zhao, Yulin|||0000-0002-4179-2409Non-autonomous differential equationLimit cyclePeriodic orbitIt is know that the non-autonomous differential equations dx/dt = a(t) + b(t)|x|, where a(t) and b(t) are 1-periodic maps of class C1, have no upper bound for their number of limit cycles (isolated solutions satisfying x(0) = x(1)). We prove that if either a(t) or b(t) does not change sign, then their maximum number of limit cycles is two, taking into account their multiplicities, and that this upper bound is sharp. We also study all possible configurations of limit cycles. Our result is similar to other ones known for Abel type periodic differential equations although the proofs are quite different. 22023-01-0120232023-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/275381https://dx.doi.org/urn:doi:10.3934/cpaa.2023016reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2019-104658GB-I00Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 CEX2020-001084-MAgència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617open 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:2753812026-06-06T12:50:31Z
dc.title.none.fl_str_mv Existence of at most two limit cycles for some non-autonomous differential equations
title Existence of at most two limit cycles for some non-autonomous differential equations
spellingShingle Existence of at most two limit cycles for some non-autonomous differential equations
Gasull, Armengol|||0000-0002-1719-8231
Non-autonomous differential equation
Limit cycle
Periodic orbit
title_short Existence of at most two limit cycles for some non-autonomous differential equations
title_full Existence of at most two limit cycles for some non-autonomous differential equations
title_fullStr Existence of at most two limit cycles for some non-autonomous differential equations
title_full_unstemmed Existence of at most two limit cycles for some non-autonomous differential equations
title_sort Existence of at most two limit cycles for some non-autonomous differential equations
dc.creator.none.fl_str_mv Gasull, Armengol|||0000-0002-1719-8231
Zhao, Yulin|||0000-0002-4179-2409
author Gasull, Armengol|||0000-0002-1719-8231
author_facet Gasull, Armengol|||0000-0002-1719-8231
Zhao, Yulin|||0000-0002-4179-2409
author_role author
author2 Zhao, Yulin|||0000-0002-4179-2409
author2_role author
dc.subject.none.fl_str_mv Non-autonomous differential equation
Limit cycle
Periodic orbit
topic Non-autonomous differential equation
Limit cycle
Periodic orbit
description It is know that the non-autonomous differential equations dx/dt = a(t) + b(t)|x|, where a(t) and b(t) are 1-periodic maps of class C1, have no upper bound for their number of limit cycles (isolated solutions satisfying x(0) = x(1)). We prove that if either a(t) or b(t) does not change sign, then their maximum number of limit cycles is two, taking into account their multiplicities, and that this upper bound is sharp. We also study all possible configurations of limit cycles. Our result is similar to other ones known for Abel type periodic differential equations although the proofs are quite different.
publishDate 2023
dc.date.none.fl_str_mv 2
2023-01-01
2023
2023-01-01
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/275381
https://dx.doi.org/urn:doi:10.3934/cpaa.2023016
url https://ddd.uab.cat/record/275381
https://dx.doi.org/urn:doi:10.3934/cpaa.2023016
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2019-104658GB-I00
Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 CEX2020-001084-M
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617
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
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eu_rights_str_mv openAccess
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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
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