On concentration of positive bound states of nonlinear Schrodinger equations with competing potential functions

Some nonlinear Schrodinger equations with several competing potential functions are considered. Ground states (least energy solutions) are proved to exist and concentrate at a point in the semiclassical limit. The concentration points are shown to be located on the middle ground of the competing potential functions and in some cases are given explicitly in terms of these functions. Also given is a necessary condition for location of concentration of positive bound states (solutions with higher but finite energy).