On Nonlinear Schrödinger Equations with Repulsive Inverse-Power Potentials.

In this paper, we consider the Cauchy problem for nonlinear Schrödinger equations with repulsive inverse-power potentials i ∂ t u + Δ u − c | x | − σ u = ± | u | α u , c > 0. <graphic href="10440_2020_382_Article_Equa.gif"></graphic> We study the local and global well-posedness, finite time blow-up and scattering in the energy space for the equation. These results extend a recent work of Miao-Zhang-Zheng (2018, ) to a general class of inverse-power potentials and higher dimensions. [ABSTRACT FROM AUTHOR]