Asymptotic behavior of periodic solutions in one-parameter families of Liénard equations

Bibliographic Details
Main Author: Cardin, Pedro Toniol [UNESP]
Publication Date: 2020
Other Authors: Novaes, Douglas Duarte
Format: Article
Language: eng
Source: Repositório Institucional da UNESP
Download full: http://dx.doi.org/10.1016/j.na.2019.111617
http://hdl.handle.net/11449/197931
Summary: In this paper, we consider one-parameter ( λ>0) families of Liénard differential equations. We are concerned with the study on the asymptotic behavior of periodic solutions for small and large values of λ>0. To prove our main result we use the relaxation oscillation theory and a topological version of the averaging theory. More specifically, the first one is appropriate for studying the periodic solutions for large values of λ and the second one for small values of λ. In particular, our hypotheses allow us to establish a link between these two theories.
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spelling Asymptotic behavior of periodic solutions in one-parameter families of Liénard equationsAveraging theoryLimit cyclesLiénard equationRelaxation oscillation theoryIn this paper, we consider one-parameter ( λ>0) families of Liénard differential equations. We are concerned with the study on the asymptotic behavior of periodic solutions for small and large values of λ>0. To prove our main result we use the relaxation oscillation theory and a topological version of the averaging theory. More specifically, the first one is appropriate for studying the periodic solutions for large values of λ and the second one for small values of λ. In particular, our hypotheses allow us to establish a link between these two theories.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) Faculdade de Engenharia, Ilha SolteiraUniversidade Estadual de Campinas (UNICAMP) Instituto de Matemática Estatística e Computação Científica CampinasUniversidade Estadual Paulista (UNESP) Faculdade de Engenharia, Ilha SolteiraFAPESP: 2013/24541-0FAPESP: 2018/13481-0FAPESP: 2018/16430-8FAPESP: 2019/00976-4FAPESP: 2019/10269-3CNPq: 306649/2018-7CNPq: 438975/2018-9CAPES: 88881.030454/2013-0Universidade Estadual Paulista (Unesp)Universidade Estadual de Campinas (UNICAMP)Cardin, Pedro Toniol [UNESP]Novaes, Douglas Duarte2020-12-12T00:54:25Z2020-12-12T00:54:25Z2020-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1016/j.na.2019.111617Nonlinear Analysis, Theory, Methods and Applications, v. 190.0362-546Xhttp://hdl.handle.net/11449/19793110.1016/j.na.2019.1116172-s2.0-85071725534Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengNonlinear Analysis, Theory, Methods and Applicationsinfo:eu-repo/semantics/openAccess2025-04-03T15:33:50Zoai:repositorio.unesp.br:11449/197931Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462025-04-03T15:33:50Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Asymptotic behavior of periodic solutions in one-parameter families of Liénard equations
title Asymptotic behavior of periodic solutions in one-parameter families of Liénard equations
spellingShingle Asymptotic behavior of periodic solutions in one-parameter families of Liénard equations
Cardin, Pedro Toniol [UNESP]
Averaging theory
Limit cycles
Liénard equation
Relaxation oscillation theory
title_short Asymptotic behavior of periodic solutions in one-parameter families of Liénard equations
title_full Asymptotic behavior of periodic solutions in one-parameter families of Liénard equations
title_fullStr Asymptotic behavior of periodic solutions in one-parameter families of Liénard equations
title_full_unstemmed Asymptotic behavior of periodic solutions in one-parameter families of Liénard equations
title_sort Asymptotic behavior of periodic solutions in one-parameter families of Liénard equations
author Cardin, Pedro Toniol [UNESP]
author_facet Cardin, Pedro Toniol [UNESP]
Novaes, Douglas Duarte
author_role author
author2 Novaes, Douglas Duarte
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
Universidade Estadual de Campinas (UNICAMP)
dc.contributor.author.fl_str_mv Cardin, Pedro Toniol [UNESP]
Novaes, Douglas Duarte
dc.subject.por.fl_str_mv Averaging theory
Limit cycles
Liénard equation
Relaxation oscillation theory
topic Averaging theory
Limit cycles
Liénard equation
Relaxation oscillation theory
description In this paper, we consider one-parameter ( λ>0) families of Liénard differential equations. We are concerned with the study on the asymptotic behavior of periodic solutions for small and large values of λ>0. To prove our main result we use the relaxation oscillation theory and a topological version of the averaging theory. More specifically, the first one is appropriate for studying the periodic solutions for large values of λ and the second one for small values of λ. In particular, our hypotheses allow us to establish a link between these two theories.
publishDate 2020
dc.date.none.fl_str_mv 2020-12-12T00:54:25Z
2020-12-12T00:54:25Z
2020-01-01
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.na.2019.111617
Nonlinear Analysis, Theory, Methods and Applications, v. 190.
0362-546X
http://hdl.handle.net/11449/197931
10.1016/j.na.2019.111617
2-s2.0-85071725534
url http://dx.doi.org/10.1016/j.na.2019.111617
http://hdl.handle.net/11449/197931
identifier_str_mv Nonlinear Analysis, Theory, Methods and Applications, v. 190.
0362-546X
10.1016/j.na.2019.111617
2-s2.0-85071725534
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Nonlinear Analysis, Theory, Methods and Applications
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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 repositoriounesp@unesp.br
_version_ 1834482548053377024

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