Teoria do grau topológico e sua aplicação em um problema elíptico ressonante superlinear

Abstract

In this work, we will show an important tool of nonlinear analysis, which has great applicability in partial differential equations: the topological degree theory. We will construct the topological degree in finite and infinite dimensions and show its main properties. Through this theory we will prove existence of solutions for two nonlinear elliptic problems with Dirichlet's boundary conditions, which were studied in [8]. To make topological degree be applicable to such problems, it will be of great importance obtain a-priori estimatives for possible solutions of these problems. To this end, we'll use inequalities of Hardy-Sobolev's type.