Blow‐up versus global well‐posedness for the focusing INLS with inverse‐square potential.

We study the focusing inhomogeneous nonlinear Schrödinger equation with inverse‐square potential i∂tu+Δu−a|x|2u+|x|−b|u|2u=0,$$ i{\partial}_tu&amp;#x0002B;\Delta u-\frac{a}{{\left&amp;#x0007C;x\right&amp;#x0007C;}&amp;#x0005E;2}u&amp;#x0002B;{\left&amp;#x0007C;x\right&amp;#x0007C;}&amp;#x0005E;{-b}{\left&amp;#x0007C;u\right&amp;#x0007C;}&amp;#x0005E;2u&amp;#x0003D;0, $$where a>−14$$ a&gt;-\frac{1}{4} $$ and 0<b<1$$ 0&lt;b&lt;1 $$ in dimension three. We extend the results of Campos and Cardoso to inhomogeneous nonlinear Schrödinger equation (INLS) with inverse‐square potential, and the proof is based on the method from Duyckaerts and Roudenko. Furthermore, our result compensates for the one of Campos and Guzmán, obtaining blow‐up versus global existence dichotomy for solutions beyond the threshold. [ABSTRACT FROM AUTHOR]