On the orbital stability for a class of nonautonomous NLS

Following the original approach introduced by T. Cazenave and P.L. Lions in [4] we prove the existence and the orbital stability of standing waves for the following class of NLS:8 n under suitable assumptions on the potentials V (x) and Q(x).More precisely we assume V (x), Q(x) ∈ L ∞ (R n ) and meas{Q(x) > λ 0 } ∈ (0, ∞) for a suitable λ 0 > 0. The main point is the analysis of the compactness of minimiziang sequences to suitable constrained minimization problems related to (0.1) and (0.2).