Equações diferenciais ordinárias generalizadas: existência, unicidade e prolongamento de soluções

Abstract

In this dissertation, we will conduct a theoretical study of some fundamental aspects of generalized ordinary differential equations (generalized ODEs). Our objective is to present important concepts and results related to these equations, with an emphasis on the theorem of existence and uniqueness of solutions for generalized ODEs with values in a Banach space. To achieve this, we provide a brief study of the Kurzweil integral, which is fundamental to this theory. Additionally, we present results on the prolongation of solutions and maximal solutions of generalized ODEs, and we describe a correspondence between measured differential equations (MDEs) and generalized ODEs, demonstrating that some results for generalized ODEs are also valid in the context of MDEs.