Existence and concentration of ground states for Schrodinger-Poisson equations with critical growth

In this paper, we study the existence and concentration behavior of ground state solutions for a class of Schrodinger-Poisson equation with a parameter epsilon > 0. Under some suitable conditions on the nonlinearity f and the potential V, we prove that for e small, the equation has a ground state solution concentrating around global minimum of the potential V in the semi-classical limit. Also, the exponential decay of the ground state solutions is studied. C (C) 2012 American Institute of Physics. [doi:10.1063/1.3683156]