Standing Waves for Nonlinear Schrödinger Equations with a General Nonlinearity.

For elliptic equations ε2Δ u − V( x) u + f( u) = 0, x ∈ 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 ε → 0, under conditions on f which we believe to be almost optimal. [ABSTRACT FROM AUTHOR]