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We consider the inhomogeneous nonlinear Schr\"odinger (INLS) equation in RN aligninls i ₜ u + u +V (x) |u|^4-2b{N}u = 0, align where V (x) = k (x) |x|^-b, with b>0. Under suitable assumptions on k (x), we established the threshold for global existence and blow-up and then study the existence and non-existence of minimal mass blow-up solutions.
Cardoso et al. (Fri,) studied this question.