Teoria do Grau e aplicações

Abstract

In this work, we will study the Topological Degree Theory that has great applicability in Ordinary Differential Equations (ODE) and Partial Differential Equations (PDE). We will construct Topological Degree Theory in three stages: In the first stage, we will construct Topological Degree in finite dimensions, more precisely, we will study Brouwer Topological Degree. In the second step we will study the Topological Degree in infinite dimension, more precisely, the Topological Degree of Leray-Schauder. In the third stage we study some applications, in which we highlight its applicability in EDP’s.