Existência de Soluções Simétricas e Não-Simétricas para uma Classe de Equações de Schrödinger Semilineares

Abstract

In this work, we establish the existence of a positive symmetric solution and a nonsymmetric solution which changes sing, for the semilinear elliptic problem ---u + V (z)u = f(z; u); u 2 H1(RN); where N - 4; V : RN ! R is a non-negative potential and f : RN-R ! R is a continuous function. To achieve these results, we use the Mountain Pass Theorem, the Principle of Symmetric Criticality and compactness results.