Propriedades Qualitativas de Soluções de Problemas Elípticos Semilineares em Domínios Não Limitados

Abstract

In this work, we study qualitative properties of solutions of the semilinear elliptic equation class 8<: u + f(u) = 0, em , u = 0, em @ , defined in different kinds of unbounded domains of Rn, among them, infinite cylinders, half spaces and Lipschitz domains. We analyze properties like convergence, monotonocity and symmetry of solutions of the problem (1), when f satisfy certain conditions suitable. For this purpose, we will use various kinds of maximum principles, the moving planes method,elliptic estimates and compacity theorems. We also studied some results about Schrödinger operators and we prove the De Giorge conjecture in dimension n = 2.