Existência de solução para uma equação de Schrodinger quasilinear

• Autor(a) principal: Ribeiro, Maico Felipe Silva
• Data de Publicação: 2010
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da Universidade Federal do Espírito Santo (riUfes)
• Texto Completo: http://repositorio.ufes.br/handle/10/6475
• topic: Teorema do passo da montanha; Matemática; Schrodinger, Equação de; Sobolev, Espaço de; 51

In this paper we study the existence of solution of a quasilinear stationary Schrodinger equation in the autonomous and nonautonomous cases. These results were demonstrated by Colin and Jeanjean. Applying a change of variables, the quasilinear equation is reduced to a semilinear one, whose associated functional is well defined in the usual Sobolev space H1(RN).The existence of solution for the autonomous case is obtained as a consequence of a result due to Berestycki and Lions. In the nonautonomous case, we show that the associated functional satisfies the mountain pass geometric hypotheses. Using a version of Mountain Pass Theorem without the compactness condition, we obtain a Cerami sequence in the minimax level weakly convergent to a solution v0. In the proof that v0 is nontrivial, the main tool is a concentration-compactness result due to Lions