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Master's Dissertation
DOI
10.11606/D.55.2019.tde-22022019-160729
Document
Author
Full name
Rita de Cássia Pavani Lamas
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1991
Supervisor
Committee
Táboas, Plácido Zoega (President)
Coelho Filho, Zaqueu Nogueira
Nunes, Wagner Vieira Leite
Title in Portuguese
Um Teorema de Periodicidade para uma Classe de Equações de Segunda Ordem com Retardamento
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Estamos interessados na equação diferencial retardada de segunda ordem x(t) + f(x(t))x(t) + g(x(t - r)) = O. (E) Nosso objetivo consiste em, seguindo o fluxo dado por (E), definir uma aplicação de retorno A sobre um conjunto fechado convexo do espaço de fase, para estudar as soluções periódicas. Para um retardamento r suficientemente pequeno, usamos um teorema de R. Nussbaum, veja Teorema(1.5), para obter a existência de soluções periódicas não constante de (E), as quais correspondem a pontos fixos não triviais de A.
Title in English
Not available
Keywords in English
Not available
Abstract in English
We are concerned with the retarded second order differential equation x(t) + f(x(t))x(t) + g(x(t - r)) = O. (E) Our aim consists in following the flow given by (E) to define a return map A on a closed convex set of the phase space, in order to study the periodic solutions. For a small delay r, we use a fixed point theorem due to R. Nussbaum, Theorem(1.5) below, to accomplish the existence of nonconstant periodic solutions of (E), which correspond to nontrivial fixed points of A.
 
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Publishing Date
2019-02-22
 
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