Existence of a ground state and scattering for a nonlinear Schroedinger equation with critical growth

Abstract

We study the energy-critical focusing nonlinear Schrödinger equation with an energy- subcritical perturbation. We show the existence of a ground state in the four or higher dimensions. Moreover, we give a sufficient and necessary condition for a solution to scatter, in the spirit of Kenig-Merle [16].

2 figures, 48 pages

References in corpus (3)

• A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation
• The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
• Existence of a ground state and blow-up problem for a nonlinear Schrodinger equation with critical growth