Soluções Radiais Positivas para Problemas Elípticos Envolvendo Crescimento Crítico

Abstract

In this work we present results of existence, non-existence and uniqueness of radial positive solutions for elliptic semilinear equations in subdomains of euclidean plane. We consider nonlinearities involving critical growth the type Trudinger- Moser. The technique used is shooting method introduced in 1905 by Severini [21]. This is a iterative method which permits determine the solution of a contour problem by analysis of approximated solutions of a family of initial value problems generated by himself. For its iteractive caracter, the shooting method it has been used effectively in applied mathematics, for exemple in the computational mathematical, where specific algorithms are used to perform such interactions. Here in an abstract approach through analytic techniques of continuity we examined whether an iteration converges to a solution of the contour problem under study.