The cubic-quintic nonlinear Schr\"odinger equation with inverse-square potential
Abstract
We consider the nonlinear Schr\"odinger 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 R.Killip, T. Oh, O. Pocovnicu, and M. Visan in the setting of the standard cubic-quintic NLS.
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