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| Author(s): |
Rodolfo Collegari
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2014-02-25 |
| Examining board members: |
Márcia Cristina Anderson Braz Federson;
Andréa Cristina Prokopczyk Arita;
Luciano Barbanti;
Miguel Vinicius Santini Frasson;
Marta Cilene Gadotti
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| Advisor: | Márcia Cristina Anderson Braz Federson |
| Abstract | |
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 (AU) | |
| FAPESP's process: | 11/01316-6 - Linear generalized differential equations and applications to retarded functional differential equations |
| Grantee: | Rodolfo Collegari |
| Support Opportunities: | Scholarships in Brazil - Doctorate (Direct) |