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

2011/12/05 by Takafumi Akahori, Slim Ibrahim, Akahori, Takafumi +5 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Energy (signal processing) #FOS: Mathematics #Ground state #Mathematical physics #Mathematics #Nonlinear Partial Differential Equations #Nonlinear Schrödinger equation #Nonlinear system #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Physics #Quantum electrodynamics #Quantum mechanics #Scattering #Schrödinger equation #Schrödinger's cat #advanced mathematical theories #math.AP

paper · pdf · doi:10.48550/arxiv.1112.1121

published in arXiv (Cornell University) (Cornell University) · 2 figures, 48 pages

arxiv created 2011/12/05 · openalex publication_date 2011/12/05 · arxiv updated 2011/12/07 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

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].

Citations

• A relation between pointwise convergence of functions and convergence of functionals

Cited by

• NLS with mass-subcritical combined nonlinearities: small mass L²-scattering

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