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Master's Dissertation
DOI
10.11606/D.55.2014.tde-23042014-163412
Document
Author
Full name
Uirá Norberto Matos de Almeida
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2014
Supervisor
Committee
Bergamasco, Adalberto Panobianco (President)
Hoepfner, Gustavo
Santos Filho, José Ruidival Soares dos
Title in Portuguese
Resolubilidade local de campos vetoriais reais
Keywords in Portuguese
Campos vetoriais
Condições de não ressonância
Linearização
Resolublidade local
Abstract in Portuguese
Nesta dissertação vamos estudar alguns importantes resultados acerca da resolubilidade local de operadores lineares de primeira ordem. Mais especificamente, seja o campo vetorial singular L em 'R POT. n' e dado por: L = '\SIGMA SUP. m' . INF. j=1' a IND. j' (x) 'SUP. \PARTIAL' INF. \PARTIAL x INF. j'. Esta trabalho dirige-se ao estudo da resolubilidade local de L, isto é, dada f 'PERTENCE A' ' C POT. INFINITO' ('R POT. n') e dado 'x IND. 0' 'PERTENCE A' 'R POT. n queremos encontrar u 'PERTENCE A' D'('R POT.n ') tal que Lu = f numa vizinhança de 'x INF. 0'. Será dada atenção especial ao caso em que os coeficientes 'a IND. j'(x) de L são função lineares. Também, serão apresentados resultados sobre a resolubilidade local da equação Lu = cu + f, sendo c 'PERTENCE A' 'C POT. INFINITO' ('R POT. n')
Title in English
Local solvability of real vector fields
Keywords in English
Linearization
Local solvability
Non-ressonance conditions
Vector fields
Abstract in English
This dissertation aims to study some important results about local solvability of first order differential operators. Specifically, let L be a singular vector field on 'R POT. n' given by L = ' \SIGMA SUP. m INF.j=1' 'a IND. j(x) '\PARTIAL SUP. INF. \PARTIAL x INF. j'. This work explore the local solvability of L, that is, given f 'IT BELONGS' 'C POT. INFINITY' ('R POT. n' and 'x INF. 0' 'IT BELONGS' 'R POT. n' we want to find u 'IT BELONGS' 2 D'('R POT. n) such that Lu = f in a neighborhood of 'x INF. 0'. We give special attention to the case where the coefficients 'a IND. j'(x) are linear. We also present some results about local solvability of the equation Lu = cu + f for c 'IT BELONGS' 'C POT. INFINITY' ('R POT. n')
 
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UiraAlmeida_revisada.pdf (746.55 Kbytes)
Publishing Date
2014-04-24
 
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