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We consider the combined power-type nonlinear Schrödinger 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.

memoirs of the american mathematical society

Global dynamics above the ground state energy for the combined power-type nonlinear Schrödinger equations with energy-critical growth at low frequencies