We consider the combined power-type nonlinear Schr¨odinger equations with energy-critical growth, and study the solutions slightly above the ground state threshold at low frequencies, so that we obtain a so-called nine-set theory developed by Nakanishi and Schlag [24, 25].

We consider the combined power-type nonlinear Schr¨odinger equations with energy-critical growth, and study the solutions slightly above the ground state threshold at low frequencies, so that we obtain a so-called nine-set theory developed by Nakanishi and Schlag [24, 25].