Abstract This paper examines the focusing nonlinear Schrödinger equation with an inverse-square potential in R N (N ≥ 3) R^N (N 3), where the nonlinear exponent lies between the mass-critical and energy-subcritical regimes. A central approach of this work is the construction of novel cross-invariant manifolds to address the challenge of proving blow-up within the potential well theory. Utilizing these manifolds, we establish a sharp threshold for the global existence and finite-time blow-up of weak solutions.
Lin et al. (Thu,) studied this question.