Existence and Non-existence of Ground State Solutions for Magnetic NLS

Oleg Asipchuk, Christopher Leonard, Shijun Zheng

Research output: Contribution to book or proceedingConference articlepeer-review

Abstract

We show the existence and stability of ground state solutions (g.s.s.) for L2-critical magnetic nonlinear Schrödinger equations (mNLS) for a class of unbounded electromagnetic potentials. We then give non-existence result by constructing a sequence of vortex type functions in the setting of RNLS with an anisotropic harmonic potential. These generalize the corresponding results in Arbunich et al. (Letters in Mathematical Physics, 109(6):1415–1432, 2019) and Van Duong Dinh (J Dyn Diff Equat, 2022). The case of an isotropic harmonic potential for rotational NLS has been recently addressed in Basharat et al. (Annales Henri Poincaré, 24(4):1377–1416, 2023). Numerical results on the ground state profile near the threshold are also included.

Original languageEnglish
Title of host publicationApplied Mathematical Analysis and Computations II - 1st SGMC
EditorsDivine Wanduku, Shijun Zheng, Zhan Chen, Andrew Sills, Haomin Zhou, Ephraim Agyingi
PublisherSpringer
Pages319-361
Number of pages43
ISBN (Print)9783031697098
DOIs
StatePublished - 2024
Event1st Southern Georgia Mathematics Conference, SGMC 2021 - Virtual, Online
Duration: Apr 2 2021Apr 3 2021

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume472
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

Conference1st Southern Georgia Mathematics Conference, SGMC 2021
CityVirtual, Online
Period04/2/2104/3/21

Scopus Subject Areas

  • General Mathematics

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