The cubic-quintic nonlinear Schr\"odinger equation with inverse-square potential

We consider the nonlinear Schrödinger equation in three space dimensions with a focusing cubic nonlinearity and defocusing quintic nonlinearity and in the presence of an external inverse-square potential. We establish scattering in the region of the mass-energy plane where the virial functional is guaranteed to be positive. Our result parallels the scattering result of [10] in the setting of the standard cubic-quintic NLS.

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