Standing waves for nonlinear Schrodinger equations with a general nonlinearity

For elliptic equations epsilon(2)Delta u-V(x) u + f(u) = 0, x is an element of R-N, N >= 3, we develop a new variational approach to construct localized positive solutions which concentrate at an isolated component of positive local minimum points of V, as epsilon -> 0, under conditions on f which we believe to be almost optimal.