TY - GEN
T1 - Existence and Non-existence of Ground State Solutions for Magnetic NLS
AU - Asipchuk, Oleg
AU - Leonard, Christopher
AU - Zheng, Shijun
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85210164459&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-69710-4_14
DO - 10.1007/978-3-031-69710-4_14
M3 - Conference article
AN - SCOPUS:85210164459
SN - 9783031697098
T3 - Springer Proceedings in Mathematics and Statistics
SP - 319
EP - 361
BT - Applied Mathematical Analysis and Computations II - 1st SGMC
A2 - Wanduku, Divine
A2 - Zheng, Shijun
A2 - Chen, Zhan
A2 - Sills, Andrew
A2 - Zhou, Haomin
A2 - Agyingi, Ephraim
PB - Springer
T2 - 1st Southern Georgia Mathematics Conference, SGMC 2021
Y2 - 2 April 2021 through 3 April 2021
ER -