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Doctoral Thesis
DOI
10.11606/T.55.2000.tde-06082001-164928
Document
Author
Full name
Selma Helena de Jesus Nicola
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2000
Supervisor
Committee
Taboas, Placido Zoega (President)
Baptistini, Margarete Teresa Zanon
Godoy, Sandra Maria Semensato de
Ragazzo, Clodoaldo Grotta
Santos, Jair Silverio dos
Title in Portuguese
Sistemas impulsivos com retardamento: soluções periódicas.
Keywords in Portuguese
ejetividade
equações diferenciais com retardamento
impulsos
soluções periódicas
teoria básica em Lp
Abstract in Portuguese
Provamos a existência de soluções periódicas de algumas equações diferenciais funcionais com retardamento sujeitas a condições de impulsos de auto-sustentação. Devido aos impulsos, soluções exibem descontinuidades de primeira espécie e isso força considerarmos espaços de fase mais gerais que C([-r,0],Rn). Mostramos que soluções periódicas podem emanar da origem através de bifurcações locais de Hopf. Também estabelecemos um teorema de existência de soluções periódicas lentamente espiralantes. Esse teorema é obtido combinando-se a condição de auto-sustentação com a ejetividade da origem em relação a um operador de retorno.
Title in English
Periodic solutions of an impulsive differential system with delay: an Lp approach.
Keywords in English
basic theory in Lp
ejectivity
impulses
periodic solutions
retarded differential equations
Abstract in English
We prove the existence of periodic solutions of some retarded functional differential equations subjected to impulsive self-supporting conditions. Due to the impulses, solutions exhibit discontinuites of the first kind and this forces the consideration of more general phase spaces than C([-r,0],Rn). We show that periodic solutions can emanate from the origin through local Hopf bifurcations. We also state an existence theorem for slowly spiralling periodic solutions. This theorem is accomplished by a combination of the self-supporting condition with the ejectivity of the origin with respect to a return operator.
 
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Selma_J_Nicola.pdf (531.16 Kbytes)
Publishing Date
2001-11-09
 
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