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In the present paper, we give some remarks on the magnetic field operators iA. As its applications, we study the Schr\"odinger equation with a magnetic field equation* - u+|A (x) |^2u+iA (x) u= u+|u|^pu, ~x R^N, equation* where u is a complex-valued function and R. When N>2, for 2 p+2 2NN-2 or N=2, for 2 p+2 +, the existence and nonexistence of minimizers of the corresponding minimization problem are given via constrained variational methods. As a by-product, the above equation admits a normalized solution. We point out that the condition divA (x) =0 plays a crucial role in our study.
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Wenbo Wang (Tue,) studied this question.
www.synapsesocial.com/papers/68e73752b6db6435876b06b1 — DOI: https://doi.org/10.59277/pra-ser.a.25.1.02
Wenbo Wang
Proceedings of the Romanian Academy Series A Mathematics Physics Technical Sciences Information Science
Yunnan University
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