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Doctoral Thesis
DOI
https://doi.org/10.11606/T.55.2011.tde-29032011-142311
Document
Author
Full name
Suzete Maria Silva Afonso
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2011
Supervisor
Committee
Federson, Márcia Cristina Anderson Braz (President)
Ferrel, Juan Bautista Limaco
Pereira, Marcone Corrêa
Slavik, Antonin
Tvrdý, Milan
Title in Portuguese
Equações diferenciais funcionais com retardamento e impulsos em tempo variável via equações diferenciais ordinárias generalizadas
Keywords in Portuguese
Equações diferenciais funcionais
Equações diferenciais ordinárias generalizadas
Impulsos
Retardamento
Abstract in Portuguese
O objetivo deste trabalho é investigar propriedades qualitativas das soluções de equações diferenciais funcionais com retardamento e impulsos em tempo variável (EDFRs impulsivas) através da teoria de equações diferenciais ordinárias generalizadas (EDOs generalizadas). Nossos principais resultados dizem respeito a estabilidade uniforme, estabilidade uniforme assintótica e estabilidade exponencial da solução trivial de uma determinada classe de EDFRs com impulsos em tempo variável e limitação uniforme de soluções da mesma classe. A fim de obtermos tais resultados para EDFRs com impulsos em tempo variável, estabelecemos novos resultados sobre propriedades qualitativas das soluções de EDOs generalizadas. Assim, portanto, este trabalho contribui para o desenvolvimento de ambas as teorias de EDFRs com impulsos e de EDOs generalizadas. Os resultados novos apresentados neste trabalho estão contidos nos artigos [1], [2] e [3]
Title in English
Retarded functional differential equations with variable impulses via generalized ordinary differential equations
Keywords in English
Delay
Functional differential equations
Generalized ordinary differential equations
Abstract in English
The purpose of this work is to investigate qualitative properties of solutions of retarded functional differential equations (RFDEs) with impulse effects acting on variable times using the theory of generalized ordinary differential equations (generalized ODEs). Our main results concern uniform stability, uniform asymptotic stability and exponential stability of the trivial solution of a certain class of RFDEs with variable impulses and uniform boundedness of the solutions of the same class. In order to obtain such results for RFDEs with variable impulses, we establish new results about qualitative properties of solutions of generalized ODEs. In this manner, we contribute with new results not only to the theory of RFDEs with impulses but also to the theory of generalized ODEs. The new results presented in this work are contained in the articles [1], [2] and [3]
 
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Publishing Date
2011-03-29
 
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