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

Hayato Nawa; Hiroaki Kikuchi; Slim Ibrahim; Takafumi Akahori

arxiv: 1112.1121 · v1 · pith:55BDVOE7new · submitted 2011-12-05 · 🧮 math.AP

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

Takafumi Akahori , Slim Ibrahim , Hiroaki Kikuchi , Hayato Nawa This is my paper

classification 🧮 math.AP

keywords equationexistencegroundnonlinearstateconditioncriticaldimensions

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

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