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Doctoral Thesis
DOI
https://doi.org/10.11606/T.55.2020.tde-19022020-111531
Document
Author
Full name
Herminio Cassago Junior
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1981
Supervisor
Committee
Onuchic, Nelson (President)
Avellar, Cerino Ewerton de
Molfetta, Natalino Adelmo de
Ribeiro, Hermano de Souza
Táboas, Plácido Zoega
Title in Portuguese
COMPORTAMENTO ASSINTÓTICO NO INFINITO ENTRE AS SOLUÇÕES DE DOIS SISTEMAS DE EQUAÇÕES DIFERENCIAIS ORDINÁRIAS
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Não disponível
Title in English
ASVYMPTOTIC BEHAVIOR AT INFINITY BETWEEN THE SOLUTIONS OF TWO SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS
Keywords in English
Not available
Abstract in English
Consider the Ordinary Differential Equations: (1) y = A(t)y + f'(t , y) (2) x = A(t)x + f2(t , x) where x, y, f' and f2(t,x) belong to X (Rn or Cn), and A(t) is an n x n matrix with t in J= [0,∞). Our objective in this work is given as follows: First, we introduce a generalization of the concept of asymptotic equivalence dealing with Banach spaces stronger than L(J,X). In addition, we give information about the number of parameters involved in the problem. Secondly, under suitable conditions, we stablish, in a natural way, homeomorphisms between a family F of D-asymptotic. solution of (1), its section F(T) and a subspace of the phase space. The above diagram, suggested by the mentioned homeomorphisms, is essentialy the one given by Taboas [18]. The main tool used here are the theorem of Corduneanu [6 - a, Th. 1] and results of Massera-Schaffer Theory [12-a,c]. Several applications of the theory under consideration are done here.
 
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Publishing Date
2020-02-19
 
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