Abstract

We prove existence and orbital stability of standing waves for the nonlinear Schrödinger equation i(latin small letter h with stroke)?2?? - V(x)? + f(l?)? in ?Nx(0,?), concentrating near a possibly degenerate local minimum of the potential V, when the Plank's constant (latin small letter h with stroke) is small enough. Our method applies to general nonlinearities, including f(s) = sp-1 with p ? (1,1 + 4/N), but does not require uniqueness nor non-degeneracy of the limiting equation.