Introdução a teoria de equações diferenciais e aplicações

Abstract

In this work we will study some topics in the theory of differential equations. We'll start by defining these equations, characterizing their solutions, and approaching classic theorems such as existence and uniqueness. The focus will then move to the study of structural stability, where we will analyze the local behavior of solutions of linear systems with constant coefficients in two dimensions, subject to disturbances in the parameters. We will also see the idea of stability introduced by Lyapunov, where we will establish conditions that will give us information about the asymptotic behavior of solutions. Finally, we will introduce the study of orbital stability with the Poincaré-Bendixson Theorem.