Scattering threshold for radial defocusing-focusing mass-energy double critical nonlinear Schrödinger equation in $d\geq 5$

We extend the scattering result for the radial defocusing-focusing mass-energy double critical nonlinear Schrödinger equation in $d\leq 4$ given by Cheng et al. to the case $d\geq 5$. The main ingredient is a suitable long time perturbation theory which is applicable for $d\geq 5$. The paper will therefore give a full characterization on the scattering threshold for the radial defocusing-focusing mass-energy double critical nonlinear Schrödinger equation in all dimensions $d\geq 3$.

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