Sobre o lema de compacidade de Strauss e aplicações

Abstract

In this work, our objective is to establish the existence of positive and radially symmetric solutions for a class of semilinear elliptic problems of the form: —Au = g (u) in RN, where N > 3, and the nonlinearity g : -+ N is a continuous function with critical N growth, satisfying conditions of the Berestycki-Lions type. To achieve this goal, we will make use of an important result in the literature known as the Strauss Compactness Lemma, which plays a fundamental role when the nonlinearity g is not necessarily a power function. Furthermore, we will prove that the obtained solution is a minimal energy solution and exhibits exponential decay.