ON THE ORBITAL STABILITY OF INHOMOGENEOUS NONLINEAR SCHRÖDINGER EQUATIONS WITH SINGULAR POTENTIAL

Abstract

We show the existence of ground state and orbital stability of standing waves of nonlinear Schrödinger equations with singular linear potential and essentially mass-subcritical power type nonlinearity. For this purpose we establish the existence of ground state in H1. We do not assume symmetry or monotonicity. We also consider local and global well-posedness of Strichartz solutions of energy-subcritical equations. We improve the range of inhomogeneous coefficient in [5, 12] slightly in 3 dimensions.