Dynamics for the energy critical nonlinear Schrödinger equation in high dimensions

In [T. Duyckaerts, F. Merle, Dynamic of threshold solutions for energy-critical NLS, preprint, arXiv:0710.5915 [math.AP]], T. Duyckaerts and F. Merle studied the variational structure near the ground state solution W of the energy critical NLS and classified the solutions with the threshold energy E(W) in dimensions d = 3, 4, 5 under the radial assumption. In this paper, we extend the results to all dimensions d 6. The main issue in high dimensions is the non-Lipschitz continuity of the nonlinearity which we get around by making full use of the decay property of W. © 2008 Elsevier Inc. All rights reserved