Electron. J. Diff. Equ., Vol. 2015 (2015), No. 296, pp. 1-15.

Existence and concentration of positive bound states for Schrodinger-Poisson systems with potential functions

Patricia L. Cunha

In this article we study the existence and concentration behavior of bound states for a nonlinear Schrodinger-Poisson system with a parameter $\varepsilon>0$. Under suitable conditions on the potential functions, we prove that for $\varepsilon$ small the system has a positive solution that concentrates at a point which is a global minimum of the minimax function associated to the related autonomous problem.

Submitted July 8, 2015. Published November 30, 2015.
Math Subject Classifications: 35B40, 35J60, 35Q55.
Key Words: Schrodinger-Poisson system; variational methods; concentration.

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Patrícia L. Cunha
Departamento de Informática e Métodos Quantitativos
Fundação Getulio Vargas
São Paulo, Brazil
email: patcunha80@gmail.com

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