Tesis Doctoral
DOI
10.11606/T.55.2014.tde-24042014-165405
Documento
Autor
Nombre completo
Rodolfo Collegari
Dirección Electrónica
Área de Conocimiento
Fecha de Defensa
Publicación
São Carlos, 2014
Director
Tribunal
Federson, Márcia Cristina Anderson Braz (Presidente)
Arita, Andréa Cristina Prokopczyk
Barbanti, Luciano
Frasson, Miguel Vinicius Santini
Título en portugués
Equações diferenciais ordinárias generalizadas lineares e aplicações às equações diferenciais funcionais lineares
Palabras clave en portugués
Equações diferenciais funcionais
Fórmula da variação das cnstantes
Resumen en portugués
Título en inglés
Linear generalized ordinary differential equations and application to linear functional differential equations
Palabras clave en inglés
Functional differential equations
Generalized ordinary differential equations
Variation of constants formula
Resumen en inglés
In this work, we present a variation-of-constants formula for linear generalized ordinary differential equations in Banach spaces. More specifically, we are interested in establishing a relation between the solutions of the Cauchy problem for a linear generalized ordinary differential equation 'dx SUP. d \tau' =D[A(t )x], x('t IND. 0') = x ('t IND. 0') = 'x SOB. ~' and the solutions of the perturbed Cauchy problem 'dx SUP. 'd \tau' =D[A(t )x +F(x, t )], x('t IND. '0) = 'x SOB.~', where the functions involved are generalized Perron integrable and, hence, admit many discontinuities and oscillations. We also prove that there exists a one-to-one correspondence between the Cauchy problem for a linear functional differential equations of the form { 'y PONTO' = L(t) 'y IND. t, 'y IND> 0 = \varphi, where L is a bounded linear operator and " is a regulated function, and a certain class of linear generalized ordinary differential equations. As a consequence, we are able to obtain a variation-of-constants formula relating the solutions of the linear functional differential equation and the solutions of the perturbed problem { 'y PONTO' = L(T)'y IND.t´+ f ('y IND. t', t), 'y IND.t IND. 0' = \varphi, where the application t 'ARROW' f('y IND. t', t) is Perron integrable, with t in an interval of R, for each regulated function y

ADVERTENCIA - La consulta de este documento queda condicionada a la aceptación de las siguientes condiciones de uso:
Este documento es únicamente para usos privados enmarcados en actividades de investigación y docencia. No se autoriza su reproducción con finalidades de lucro. Esta reserva de derechos afecta tanto los datos del documento como a sus contenidos. En la utilización o cita de partes del documento es obligado indicar el nombre de la persona autora.