Periodic solutions of linear, Riccati, and Abel dynamic equations

We study the number of periodic solutions of linear, Riccati and Abel dynamic equations in the time scales setting. In this way, we recover known results for corresponding differential equations and obtain new results for associated difference equations. In particular, we prove that there is no uppe...

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Autores: Bohner, Martin|||0000-0001-8310-0266, Gasull, Armengol|||0000-0002-1719-8231, Valls, Clàudia|||0000-0001-8279-1229
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:204401
Acceso en línea:https://ddd.uab.cat/record/204401
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2018.10.018
Access Level:acceso abierto
Palabra clave:Linear
Riccati and Abel differential and difference equations
Time scales
Periodic function
Melnikov function
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spelling Periodic solutions of linear, Riccati, and Abel dynamic equationsBohner, Martin|||0000-0001-8310-0266Gasull, Armengol|||0000-0002-1719-8231Valls, Clàudia|||0000-0001-8279-1229LinearRiccati and Abel differential and difference equationsTime scalesPeriodic functionMelnikov functionWe study the number of periodic solutions of linear, Riccati and Abel dynamic equations in the time scales setting. In this way, we recover known results for corresponding differential equations and obtain new results for associated difference equations. In particular, we prove that there is no upper bound for the number of isolated periodic solutions of Abel difference equations. One of the main tools introduced to get our results is a suitable Melnikov function. This is the first time that Melnikov functions are used for dynamic equations on time scales. 22019-01-0120192019-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/204401https://dx.doi.org/urn:doi:10.1016/j.jmaa.2018.10.018reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2016-77278-PAgència 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:2044012026-06-06T12:50:31Z
dc.title.none.fl_str_mv Periodic solutions of linear, Riccati, and Abel dynamic equations
title Periodic solutions of linear, Riccati, and Abel dynamic equations
spellingShingle Periodic solutions of linear, Riccati, and Abel dynamic equations
Bohner, Martin|||0000-0001-8310-0266
Linear
Riccati and Abel differential and difference equations
Time scales
Periodic function
Melnikov function
title_short Periodic solutions of linear, Riccati, and Abel dynamic equations
title_full Periodic solutions of linear, Riccati, and Abel dynamic equations
title_fullStr Periodic solutions of linear, Riccati, and Abel dynamic equations
title_full_unstemmed Periodic solutions of linear, Riccati, and Abel dynamic equations
title_sort Periodic solutions of linear, Riccati, and Abel dynamic equations
dc.creator.none.fl_str_mv Bohner, Martin|||0000-0001-8310-0266
Gasull, Armengol|||0000-0002-1719-8231
Valls, Clàudia|||0000-0001-8279-1229
author Bohner, Martin|||0000-0001-8310-0266
author_facet Bohner, Martin|||0000-0001-8310-0266
Gasull, Armengol|||0000-0002-1719-8231
Valls, Clàudia|||0000-0001-8279-1229
author_role author
author2 Gasull, Armengol|||0000-0002-1719-8231
Valls, Clàudia|||0000-0001-8279-1229
author2_role author
author
dc.subject.none.fl_str_mv Linear
Riccati and Abel differential and difference equations
Time scales
Periodic function
Melnikov function
topic Linear
Riccati and Abel differential and difference equations
Time scales
Periodic function
Melnikov function
description We study the number of periodic solutions of linear, Riccati and Abel dynamic equations in the time scales setting. In this way, we recover known results for corresponding differential equations and obtain new results for associated difference equations. In particular, we prove that there is no upper bound for the number of isolated periodic solutions of Abel difference equations. One of the main tools introduced to get our results is a suitable Melnikov function. This is the first time that Melnikov functions are used for dynamic equations on time scales.
publishDate 2019
dc.date.none.fl_str_mv 2
2019-01-01
2019
2019-01-01
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/204401
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2018.10.018
url https://ddd.uab.cat/record/204401
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2018.10.018
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2016-77278-P
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
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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
reponame_str Dipòsit Digital de Documents de la UAB
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