Long time dynamics of the 3D radial NLS with the combined terms

In this paper, we study the scattering and blow-up dichotomy result of the radial solution to nonlinear Schrödinger equation (NLS) with the combined terms iu_t +Δu= -|u|⁴u + |u|^p-1u, 1 +4/3< p < 5 in energy space H¹(R³). The threshold energy is the energy of the ground state W of the focusing, energy critical NLS, which means that the subcritical perturbation does not affect the determination of threshold, but affects the scattering and blow-up dichotomy result with subcritical threshold energy. This extends algebraic perturbation in a previous work of Miao, Xu and Zhao Comm. Math. Phys., 318, 767-808 (2013)] to all mass supercritical, energy subcritical perturbation.