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

Abstract

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.

24 pages