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Master's Dissertation
DOI
https://doi.org/10.11606/D.55.2020.tde-19022020-144649
Document
Author
Full name
Mara Sueli Simao Moraes
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1981
Supervisor
Committee
Táboas, Plácido Zoega (President)
Carvalho, Luiz Antonio Vieira de
Rodrigues, Sergio
Title in Portuguese
BIFURCAÇÃO DE SOLUÇÕES PERIÓDICAS DE UM OSCILADOR NÃO LINEAR AMORTECIDO E FORÇADO
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Não disponível
Title in English
Not available
Keywords in English
Not available
Abstract in English
Suppose the equation x + g(x) = -λ1x + λ2f where f is a scalar function which is 2π-periodic, λ1, λ2 are real parameters, xg(x) > 0 for x ≠ 0. The initial problem is to Characterize the existence and the number of 2π-periodic solutions of (1) which lie in a neighborhood of a 2π-periodic orbit of the degenerated equation x + g(x) = 0 (2) whose orbit in the (x, x) - space encircles the origin. The Liapunov-Schmidt reduction method is applied to obtain the bifurcation equations. The results are then obtained by successive use of the Implict Function theorenm,. We also characterize the existence and the number of 4π-periodic solutions of (1) which lie in a neighborhood of a 2π-periodic orbit of (2).
 
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Publishing Date
2020-02-19
 
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