Dissertação de Mestrado Acadêmico - Francisca Mafiza M. A. Silva

Title: Asymptotic Stability of Solutions in Systems of Ordinary Differential Equations

Abstract: This dissertation investigates asymptotic stability in three classes of ODE systems. For linear systems x′ = Ax, it is shown that eigenvalues with negative real parts guarantee stability, while some eigenvalues with positive real parts imply instability. For nonlinear systems x′ = Ax + f(t, x) with ||f(t, x)|| = o(||x||), analysis via linearization extends these results locally. For autonomous systems, it is shown that the decomposition F(x) = Ax + f(x) reduces the problem to the nonlinear case. The work uses properties of the matrix exponential to support this unified approach, as well as concepts, propositions, and theorems from Linear Algebra, Analysis on the Real Line, and in the space Rn.

Orientador: Boyan Slavchev Sirakov - PUC-Rio

Banca examinadora:
Silvius Klein - PUC-Rio
Rangel Baldasso - PUC-Rio
Carlos Manuel Guzmán Jiménez - UFF
Cleyton Natanael Lopes de Carvalho Cunha - UFDPAR

Data: 29 de abril de 2026
Horário: 10h 
Sala: L856