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

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

2011-12-05

arxiv.org/abs/1112.1121v1

Mathematics

Analysis of PDEs

2 figures, 48 pages

Scientific paper

We study the energy-critical focusing nonlinear Schr\"odinger 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].

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