Existência de solução de energia mínima para uma equação de Schrödinger não linear
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Data
2012-03-06
Autores
Rocha, Karlo Fernandes
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Universidade Federal do Espírito Santo
Resumo
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