Aplicações dos teoremas de ponto fixo para equações diferenciais parciais

Abstract

In this work, we present and prove the fixed-point theorems of Banach, Schauder, and Schaefer, and the later we applied in the resolution of three nonlinear problems, we also study the Sobolev Spaces, fundamental for testing the existence and uniqueness of soluti ons in Partial Differential Equations. The Banach Fixed-Point Theorem for contractions is applied to prove the existence of a solution in a diffusion and reaction system, whereas the fixed-point theorems of Schauder and Schaefer are used to solve two problems of el liptic equations, respectively, semilinear and quasilinear.