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| Author(s): |
Lucas Henrique Destro de Toledo
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2023-02-17 |
| Examining board members: |
Everaldo de Mello Bonotto;
Suzete Maria Silva Afonso;
Andréa Cristina Prokopczyk Arita;
Karina Schiabel
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| Advisor: | Everaldo de Mello Bonotto |
| Abstract | |
The theory of generalized ordinary differential equations or simply GODEs is a theory of differential equations in Banach spaces which deals with functions that have many discontinuities and (or) are of unbounded variation. In this context, if X denotes a Banach space, we present the concept of exponential dichotomy for GODEs of the form dx d = D[A(t)x], where A : R L(X) is an operator, and we exhibit sufficient conditions for the existence and uniqueness of bounded (and T periodic) solutions for the perturbed problem dx d = D[A(t)x+ f(t)], where the operators A : R L(X) and f : R L(X) satisfy specific conditions. In addition, we apply the obtained results to other types of differential equations: measure differential equations (MDEs) and impulsive differential equations (IDEs). (AU) | |
| FAPESP's process: | 20/14444-1 - Dichotomies in generalized ordinary differential equations |
| Grantee: | Lucas Henrique Destro de Toledo |
| Support Opportunities: | Scholarships in Brazil - Master |