ABSTRACT
For many given ODE models, it is not possible to construct their solutions by integration methods, and this fact poses the question whether a solution exists and if it is unique under certain conditions. These are the topics of this chapter, where proofs of existence and uniqueness of solutions are presented, starting from the theory of Peano and concluding with that of Carathéodory. The main tools for this analysis are Euler’s method and the Arzelà-Ascoli theorem.
