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Doctoral Thesis
DOI
10.11606/T.55.2018.tde-27112018-154151
Document
Author
Full name
Luiz Fernandes Galante
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1991
Supervisor
Committee
Rodrigues, Hildebrando Munhoz (President)
Ize, Antonio Fernandes
Lopes, Orlando Francisco
Menzala, Gustavo Perla
Nascimento, Arnaldo Simal do
Title in Portuguese
SOBRE BIFURCAÇÃO E SIMETRIA EM EQUAÇÕES NÃO LINEARES
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Neste trabalho estudamos existência bifurcação e simetrias de soluções especiais de equações não-lineares da forma: (1) Lx = N(x, p, ε) + μf, as quais são equivariantes sob a aço de certos grupos de simetrias. Assumimos que a equação (1) esta definida num espaço de Banach X, f é um elemento fixo de um espaço de Banach Z, L é um operador linear e continuo de X em Z, N é um operador não linear, p, μ e ε são pequenos parâmetros. Sob certas hipóteses mostramos que simetrias do termo forçante implicam em simetrias das pequenas soluções da equação acima. Discutimos também a genericidade da principal hipótese deste trabalho. Alguns exemplos envolvendo equações diferenciais ordinárias e parciais são analisados.
Title in English
Not available
Keywords in English
Not available
Abstract in English
The object of this work is to study existence and bifurcation of special solutions of a nonlinear equations: Lx = N(x, p ,ε) + μf, defined in a Banach space X, which is equivariant under the action of a certain symmetry groups. It is assumed that L is a continuous linear operator, N is a nonlinear operator, the forcing term f is an element of a Banach space Z, p, μ and ε are small parameters. Under certain hypothesis it is shown that:symmetries of the forcing term f imply symmetries of the small solu tions of the above nonlinear equations. It is also discussed the genericity of the main hy pothesis of this work. Some examples involving either ordinary differential equations or partial equations are also analised.
 
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Publishing Date
2018-11-27
 
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