Scattering and blow-up solutions to nonlinear Schrödinger equation beyond the threshold

In this paper, we consider nonlinear Schrödinger equation. Duyckaerts–Roudenko [Comm. Math. Phys. 334 (2015), no. 3, 1573–1615] investigated time behavior of solutions to the equation, whose mass-energy is greater than that of the ground state. We revisit the results and show by using the action. Moreover, we apply it to other equations without scale invariance.