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| Author(s): |
Fábio Lima Santos
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: | 2016-12-16 |
| Examining board members: |
Everaldo de Mello Bonotto;
Ma To Fu;
Marta Cilene Gadotti;
Marcelo José Dias Nascimento;
Bruno Luis de Andrade Santos
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| Advisor: | Márcia Cristina Anderson Braz Federson |
| Abstract | |
In this work we establish the theory of dichotomies for generalized ordinary dierential equations, introducing the concepts of dichotomies for these equations, studying their properties and proposing new results. We investigate conditions of existence of exponential dichotomies and bounded solutions. Using correspondence theorems between generalized ordinary dierential equations and other equations, we translate the obtained results to the particular cases of dichotomies for measure dierential equations and for impulsive dierential equations. The fact that we work in the framework of generalized ordinary dierential equations allows us to obtain results for the particular cases where the functions involved can have many discontinuities and be of unbounded variation. (AU) | |
| FAPESP's process: | 11/24027-0 - Dichotomies in generalized differential equations and applications |
| Grantee: | Fábio Lima Santos |
| Support Opportunities: | Scholarships in Brazil - Doctorate |