Abstract
By deriving a variant of interpolation inequality, we obtain a sharp criterion for global existence and blow-up of solutions to the inhomogeneous nonlinear Schrodinger equation with harmonic potential $$ i\phi t = - \Delta \phi + \left| x \right|^2 \phi - \left| x \right|^b \left| \phi \right|^{p - 2} \phi $$ . We also prove the existence of unstable standing-wave solutions via blow-up under certain conditions on the unbounded inhomogeneity and the power of nonlinearity, as well as the frequency of the wave.
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