Periodic solutions of Lienard differential equations via averaging theory of order two

Detalhes bibliográficos
Autor(a) principal: LLIBRE,JAUME
Data de Publicação: 2015
Outros Autores: NOVAES,DOUGLAS D., TEIXEIRA,MARCO A.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Anais da Academia Brasileira de Ciências (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652015000501905
Resumo: Abstract For ε ≠ 0sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the form x ′′ + f ⁢ ( x ) ⁢ x ′ + n 2 ⁢ x + g ⁢ ( x ) = ε 2 ⁢ p 1 ⁢ ( t ) + ε 3 ⁢ p 2 ⁢ ( t ) , where n is a positive integer, f : ℝ → ℝis a C 3function, g : ℝ → ℝis a C 4function, and p i : ℝ → ℝfor i = 1 , 2are continuous 2 ⁢ π–periodic function. The main tool used in this paper is the averaging theory of second order. We also provide one application of the main result obtained.
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spelling Periodic solutions of Lienard differential equations via averaging theory of order twoperiodic solutionLienard differential equationaveraging theorybifurcation theoryAbstract For ε ≠ 0sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the form x ′′ + f ⁢ ( x ) ⁢ x ′ + n 2 ⁢ x + g ⁢ ( x ) = ε 2 ⁢ p 1 ⁢ ( t ) + ε 3 ⁢ p 2 ⁢ ( t ) , where n is a positive integer, f : ℝ → ℝis a C 3function, g : ℝ → ℝis a C 4function, and p i : ℝ → ℝfor i = 1 , 2are continuous 2 ⁢ π–periodic function. The main tool used in this paper is the averaging theory of second order. We also provide one application of the main result obtained.Academia Brasileira de Ciências2015-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652015000501905Anais da Academia Brasileira de Ciências v.87 n.4 2015reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/0001-3765201520140129info:eu-repo/semantics/openAccessLLIBRE,JAUMENOVAES,DOUGLAS D.TEIXEIRA,MARCO A.eng2015-12-11T00:00:00Zoai:scielo:S0001-37652015000501905Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2015-12-11T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false
dc.title.none.fl_str_mv Periodic solutions of Lienard differential equations via averaging theory of order two
title Periodic solutions of Lienard differential equations via averaging theory of order two
spellingShingle Periodic solutions of Lienard differential equations via averaging theory of order two
LLIBRE,JAUME
periodic solution
Lienard differential equation
averaging theory
bifurcation theory
title_short Periodic solutions of Lienard differential equations via averaging theory of order two
title_full Periodic solutions of Lienard differential equations via averaging theory of order two
title_fullStr Periodic solutions of Lienard differential equations via averaging theory of order two
title_full_unstemmed Periodic solutions of Lienard differential equations via averaging theory of order two
title_sort Periodic solutions of Lienard differential equations via averaging theory of order two
author LLIBRE,JAUME
author_facet LLIBRE,JAUME
NOVAES,DOUGLAS D.
TEIXEIRA,MARCO A.
author_role author
author2 NOVAES,DOUGLAS D.
TEIXEIRA,MARCO A.
author2_role author
author
dc.contributor.author.fl_str_mv LLIBRE,JAUME
NOVAES,DOUGLAS D.
TEIXEIRA,MARCO A.
dc.subject.por.fl_str_mv periodic solution
Lienard differential equation
averaging theory
bifurcation theory
topic periodic solution
Lienard differential equation
averaging theory
bifurcation theory
description Abstract For ε ≠ 0sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the form x ′′ + f ⁢ ( x ) ⁢ x ′ + n 2 ⁢ x + g ⁢ ( x ) = ε 2 ⁢ p 1 ⁢ ( t ) + ε 3 ⁢ p 2 ⁢ ( t ) , where n is a positive integer, f : ℝ → ℝis a C 3function, g : ℝ → ℝis a C 4function, and p i : ℝ → ℝfor i = 1 , 2are continuous 2 ⁢ π–periodic function. The main tool used in this paper is the averaging theory of second order. We also provide one application of the main result obtained.
publishDate 2015
dc.date.none.fl_str_mv 2015-12-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652015000501905
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652015000501905
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/0001-3765201520140129
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Academia Brasileira de Ciências
publisher.none.fl_str_mv Academia Brasileira de Ciências
dc.source.none.fl_str_mv Anais da Academia Brasileira de Ciências v.87 n.4 2015
reponame:Anais da Academia Brasileira de Ciências (Online)
instname:Academia Brasileira de Ciências (ABC)
instacron:ABC
instname_str Academia Brasileira de Ciências (ABC)
instacron_str ABC
institution ABC
reponame_str Anais da Academia Brasileira de Ciências (Online)
collection Anais da Academia Brasileira de Ciências (Online)
repository.name.fl_str_mv Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)
repository.mail.fl_str_mv ||aabc@abc.org.br
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