Minimax Theory and its Applications 06 (2021), No. 1, 025--060
Copyright Heldermann Verlag 2021
Concentration of Semi-Classical States for Nonlinear Dirac Equations of Space-Dimension n
Yanheng Ding
Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China
dingyh@math.ac.cn
Qi Guo
University of the Chinese Academy of Sciences, Beijing 100049, P. R. China, Jiangsu, China
guoqi115@mails.ucas.ac.cn
Tian Xu
Center for Applied Mathematics, Tianjin University, Tianjin 300072, P. R. China
xutian@amss.ac.cn
We study the semi-classical approximation of a massive Dirac equation in space-dimension n ≥ 2 with some general nonlinear self-coupling. We prove that there exists a family of ground states of the semi-classical problem, for all h small, and show that the family concentrates around some certain sets determined by the competing potential functions as h approaches 0.
Keywords: Dirac equations, semi-classical states, concentration.
MSC: 35B25, 35Q40, 49J35.
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