Existência de solução de energia mínima para uma equação de Schrödinger não linear

Abstract

In this work we study the existence of solution of a quasilinear Schr¨odinger equation in R N , demonstrated by Ruiz and Siciliano. By working in an appropriated functions space, by using a variational identity demonstrated by Pucci and Serrin, a set M containing all nontrivial solutions of the equation is obtained. By using a concentrationcompactness result due to Lions, it is possible to prove that the infimum of the functional associated with the equation, restricted to the set M, is achieved at some u which is a positive ground state solution