LAUSR

We consider the stability of standing waves for the focusing nonlinear Schrodinger equation with an inverse-square potential. Using the profile decomposition arguments, we show that in the L2-subcritical case, i.e., 0<α<4d, the sets of ground state standing waves are orbitally stable. In the L2-critical case, i.e., α=4d, we show that ground state standing waves are strongly unstable by blow-up.We consider the stability of standing waves for the focusing nonlinear Schrodinger equation with an inverse-square potential. Using the profile decomposition arguments, we show that in the L2-subcritical case, i.e., 0<α<4d, the sets of ground state standing waves are orbitally stable. In the L2-critical case, i.e., α=4d, we show that ground state standing waves are strongly unstable by blow-up.