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Master's Dissertation
DOI
https://doi.org/10.11606/D.55.1970.tde-27062022-151252
Document
Author
Full name
Hildebrando Munhoz Rodrigues
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1970
Supervisor
Committee
Onuchic, Nelson (President)
Loibel, Gilberto Francisco
Oliva, Waldyr Muniz
Title in Portuguese
INVARIANÇA PARA SISTEMAS NÃO AUTÔNOMOS DE EQUAÇÕES DIFERENCIAIS COM RETARDAMENTO E APLICAÇÕES
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Não disponível
Title in English
Invariance properties in the theory of differential equations with time delay and applications
Keywords in English
Not available
Abstract in English
This work is essentially diuided in two parts. In the first part we introduce the concept of ínvariant set with respect to a nonautonomous delay equation (I) y(t) = P(t, yt). Consider the perturbed equation (2) x(t) = P(t, xt) + Q(t, xt) + S(t, xt) where Q and are "small" perturbations in a sence specified in this work. With respect to the concept of invariante, as introduced in the first part, the following property holdes: The ω-limit set of every solution x(t) of (2), bounded in the future, is invariant with respect to (1). In the second part, the following application of the above mentioned theory is done: Consider the equations (I) x + f(t, x, x) + g(x) = 0 (II) x + f(t, x, x) + g(x) + h(t, x, x) = 0 By using the concept of invariance with respect to (I), we obtain, under certain assumptions on f, g and h, some stability results concerning equation (II).
 
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Publishing Date
2022-06-27
 
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