O Grau de Coincidência e aplicação às equações diferenciais ordinárias periódicas

Abstract

In this work, we will present the coincident degree theory for Fredholm operators of index zero - denoted by L and defined on Banach spaces -, which is an important tool to obtain the existence of solutions for equations of the type Lx=Nx in an open bounded set Omega, N being a L-compact operator. Throughout this theory, we will investigate the existence of solutions of an Ambrosetti-Prodi periodic problem for non-linear ordinary differential equations. In order to apply the topological degree in such problem, obtaining a priori estimates for possible solutions will be of great importance.