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Doctoral Thesis
DOI
https://doi.org/10.11606/T.55.1978.tde-31102022-174730
Document
Author
Full name
Luiz Carlos Paulu
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1978
Supervisor
Committee
Onuchic, Nelson (President)
Basta, Cesar
Lopes, Orlando Francisco
Molfetta, Natalino Adelmo de
Táboas, Plácido Zoega
 
Title in Portuguese
FUNÇÕES DE LIAPUNOV E PROPRIEDADES DE INVARIÂNCA PARASISTEMAS NÃO AUTÔNOMOS: ESTABILIDADE E INSTABILIDADE
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Não disponível
 
Title in English
Not available
Keywords in English
Not availale
Abstract in English
This work has two distincts objectives. However these objectives are basically dependents on the invariance properties of /ω-limit sets of solutions, bounded in the future, of differential equations. The first objective is essentially an application of the above mentioned result. We look for conditions under which, we can guarantee that every solution (x(t),x(t)), of a nonautonomous second order differential equation. x + h(t,x,x)x + f(x) + g(t,x,x) + p(t,x,x) = 0, tends to (n,0), as t →, ∞, where (n,0) is an equilibrium point of a certain autonomous equation. We are also interested in studying the stability properties of a class of equilibrium point of the above mentioned second order differential equation. Our results are closely related to the ones obtained by N.0nuchic in [11]. However our hypotheses are different from his assump- tions. The second main objective of this work is to extend criterions of instability obtained by N.0nuchic [13] to a certain class of nonautonomous differential systems. To this end the main tool used here is provided by results of H.M.Rodrigues [16] on Invariance.
 
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Publishing Date
2022-10-31
 
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