Doctoral Thesis
DOI
https://doi.org/10.11606/T.55.1973.tde-29062022-095210
Document
Author
Full name
Hildebrando Munhoz Rodrigues
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1973
Supervisor
Committee
Onuchic, Nelson (President)
Ize, Antonio Fernandes
Lopes, Orlando Francisco
Oliva, Waldyr Muniz
Vieira, Leo Roberto Borges
Title in Portuguese
EQUIVALÊNCIA ASSINTÓTICA RELATIVA, COM PESO tµ , ENTRE DOIS SISTEMAS D EQUAÇÕOES DIFERENCIAIS ORDINÁRIAS
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Não disponível
Title in English
RELATIVE ASYMPTOTIC EQUIVALENCEL WITH WEIGHT tµ BETWEEN TWO SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS
Keywords in English
Not available
Abstract in English
We organize this work as follows: In first part we study the relative asymptotic equivalence, with weight tµ, where µ is a non negative integer number, of systems: (a) y = A(t)y (b) x = A(t)x + f(t, x), namely, we prove that under certain assumptions, the followings results hold: 1) For every solution y(t)≠ O of (a) there is at least one solution x(t) of (b) satisfying: (c) tµ ΙΙ x (t) - y(t) ΙΙ / ΙΙ y (t) → 0, as t → 0 ∞ For every solution x(t) of (b), x(t); ≠ O for all sufficiently large t, there corresponds at least one solution y(t) of (a) satisfying (c). We also give information about the number of parameters of the family of solutions x(t) of (b) satisfying 1). A similar result follows with respect condition. 2) In second part we apply the above mentioned results to a class of matrices A(t) which contains the periodic and constant matrices as particular cases.
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Publishing Date
2022-06-29