Existence and uniqueness of limit cycles for generalized phi-Laplacian Lienard equations
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.jmaa.2016.03.004 http://hdl.handle.net/11449/161453 |
Resumo: | The Lienard equation x + f (x)x' + g(x) = 0 appears as a model in many problems of science and engineering. Since the first half of the 20th century, many papers have appeared providing existence and uniqueness conditions for limit cycles of Lienard equations. In this paper we extend some of these results for the case of the generalized phi-Laplacian Lienard equation, (phi(x'))' f(x)psi(x') + g(x) = 0. This generalization appears when derivations of the equation different from the classical one are considered. In particular, the relativistic van der Pol equation, (x'/root 1 - (x'/c)(2))' + mu(x(2) - 1)x' + x = 0, has a unique periodic orbit when mu = 0. (C) 2016 Elsevier Inc. All rights reserved. |
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Existence and uniqueness of limit cycles for generalized phi-Laplacian Lienard equationsExistence and uniquenessPeriodic orbitsLimit cyclesphi-Laplacian Lienard equationsGeneralized Lienard. equationsThe Lienard equation x + f (x)x' + g(x) = 0 appears as a model in many problems of science and engineering. Since the first half of the 20th century, many papers have appeared providing existence and uniqueness conditions for limit cycles of Lienard equations. In this paper we extend some of these results for the case of the generalized phi-Laplacian Lienard equation, (phi(x'))' f(x)psi(x') + g(x) = 0. This generalization appears when derivations of the equation different from the classical one are considered. In particular, the relativistic van der Pol equation, (x'/root 1 - (x'/c)(2))' + mu(x(2) - 1)x' + x = 0, has a unique periodic orbit when mu = 0. (C) 2016 Elsevier Inc. All rights reserved.MINECOCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)MINECO/FEDERGeneralitat de CatalunyaEuropean CommunityUniv Estadual Paulista, Dept Matemat, Rua Cristovao Colombo 2265, BR-15054000 Sao Jose Do Rio Preto, SP, BrazilUniv Autonoma Barcelona, Dept Matemat, Edifici C, E-08193 Barcelona, SpainUniv Granada, Dept Matemat Aplicada, E-18071 Granada, SpainUniv Estadual Paulista, Dept Matemat, Rua Cristovao Colombo 2265, BR-15054000 Sao Jose Do Rio Preto, SP, BrazilMINECO: MTM2013-40998-PCAPES: 1271113MINECO/FEDER: UNAB13-4E-1604MINECO/FEDER: MTM2014-52232-PMINECO/FEDER: FQM-1861Generalitat de Catalunya: 2014SGR568European Community: FP7-PEOPLE-2012-IRSES-318999European Community: FP7-PEOPLE-2012-IRSES-316338Elsevier B.V.Universidade Estadual Paulista (Unesp)Univ Autonoma BarcelonaUniv GranadaPerez-Gonzalez, S. [UNESP]Torregrosa, J.Torres, P. J.2018-11-26T16:32:48Z2018-11-26T16:32:48Z2016-07-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article745-765application/pdfhttp://dx.doi.org/10.1016/j.jmaa.2016.03.004Journal Of Mathematical Analysis And Applications. San Diego: Academic Press Inc Elsevier Science, v. 439, n. 2, p. 745-765, 2016.0022-247Xhttp://hdl.handle.net/11449/16145310.1016/j.jmaa.2016.03.004WOS:000374918500019WOS000374918500019.pdfWeb of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal Of Mathematical Analysis And Applicationsinfo:eu-repo/semantics/openAccess2023-12-06T06:18:47Zoai:repositorio.unesp.br:11449/161453Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-12-06T06:18:47Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Existence and uniqueness of limit cycles for generalized phi-Laplacian Lienard equations |
title |
Existence and uniqueness of limit cycles for generalized phi-Laplacian Lienard equations |
spellingShingle |
Existence and uniqueness of limit cycles for generalized phi-Laplacian Lienard equations Perez-Gonzalez, S. [UNESP] Existence and uniqueness Periodic orbits Limit cycles phi-Laplacian Lienard equations Generalized Lienard. equations |
title_short |
Existence and uniqueness of limit cycles for generalized phi-Laplacian Lienard equations |
title_full |
Existence and uniqueness of limit cycles for generalized phi-Laplacian Lienard equations |
title_fullStr |
Existence and uniqueness of limit cycles for generalized phi-Laplacian Lienard equations |
title_full_unstemmed |
Existence and uniqueness of limit cycles for generalized phi-Laplacian Lienard equations |
title_sort |
Existence and uniqueness of limit cycles for generalized phi-Laplacian Lienard equations |
author |
Perez-Gonzalez, S. [UNESP] |
author_facet |
Perez-Gonzalez, S. [UNESP] Torregrosa, J. Torres, P. J. |
author_role |
author |
author2 |
Torregrosa, J. Torres, P. J. |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Univ Autonoma Barcelona Univ Granada |
dc.contributor.author.fl_str_mv |
Perez-Gonzalez, S. [UNESP] Torregrosa, J. Torres, P. J. |
dc.subject.por.fl_str_mv |
Existence and uniqueness Periodic orbits Limit cycles phi-Laplacian Lienard equations Generalized Lienard. equations |
topic |
Existence and uniqueness Periodic orbits Limit cycles phi-Laplacian Lienard equations Generalized Lienard. equations |
description |
The Lienard equation x + f (x)x' + g(x) = 0 appears as a model in many problems of science and engineering. Since the first half of the 20th century, many papers have appeared providing existence and uniqueness conditions for limit cycles of Lienard equations. In this paper we extend some of these results for the case of the generalized phi-Laplacian Lienard equation, (phi(x'))' f(x)psi(x') + g(x) = 0. This generalization appears when derivations of the equation different from the classical one are considered. In particular, the relativistic van der Pol equation, (x'/root 1 - (x'/c)(2))' + mu(x(2) - 1)x' + x = 0, has a unique periodic orbit when mu = 0. (C) 2016 Elsevier Inc. All rights reserved. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-07-15 2018-11-26T16:32:48Z 2018-11-26T16:32:48Z |
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.jmaa.2016.03.004 Journal Of Mathematical Analysis And Applications. San Diego: Academic Press Inc Elsevier Science, v. 439, n. 2, p. 745-765, 2016. 0022-247X http://hdl.handle.net/11449/161453 10.1016/j.jmaa.2016.03.004 WOS:000374918500019 WOS000374918500019.pdf |
url |
http://dx.doi.org/10.1016/j.jmaa.2016.03.004 http://hdl.handle.net/11449/161453 |
identifier_str_mv |
Journal Of Mathematical Analysis And Applications. San Diego: Academic Press Inc Elsevier Science, v. 439, n. 2, p. 745-765, 2016. 0022-247X 10.1016/j.jmaa.2016.03.004 WOS:000374918500019 WOS000374918500019.pdf |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Journal Of Mathematical Analysis And Applications |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
745-765 application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier B.V. |
publisher.none.fl_str_mv |
Elsevier B.V. |
dc.source.none.fl_str_mv |
Web of Science 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_ |
1797789922918137856 |