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| Author(s): |
Giselle Antunes Monteiro
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: | 2012-02-14 |
| Examining board members: |
Márcia Cristina Anderson Braz Federson;
Luciano Barbanti;
Ma To Fu;
Claudio Rodrigo Cuevas Henriquez;
Suzinei Aparecida Siqueira Marconato
|
| Advisor: | Márcia Cristina Anderson Braz Federson |
| Abstract | |
The purpose of this work is to investigate continuous dependence on parameters for generalized linear differential equations in a Banach space- valued setting. More precisely, we establish a theorem inspired by the clas- sical continuous dependence result due to Z. Opial. In addition, our second outcome extends, to Banach spaces, the result proved by M. Ashordia in the framework of finite dimensional generalized linear differential equations. Roughly speaking, the continuous dependence derives from assumptions of uniform convergence of the functions in the right-hand side of the equations, together with the uniform boundedness of variation of the linear terms. Fur- thermore, applications of these results to dynamic equations on time scales and also to functional differential equations are proposed. Besides these results on continuous dependence, we complete the theory of abstract Kurzweil-Stieltjes integration so that it is well applicable for our purposes in generalized linear differential equations. In view of this, our contributions are related not only to differential equations but also to the abstract Kurzweil-Stieltjes integration theory itself. The new results presented in this work are contained in the papers [26] and [27], both accepted for publication (AU) | |
| FAPESP's process: | 11/06392-2 - Generalized Linear Differential Equations: continuous dependence and applications to Functional Differential Equations |
| Grantee: | Giselle Antunes Monteiro |
| Support Opportunities: | Scholarships in Brazil - Doctorate |