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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

Qi Guo
University of the Chinese Academy of Sciences, Beijing 100049, P. R. China, Jiangsu, China

Tian Xu
Center for Applied Mathematics, Tianjin University, Tianjin 300072, P. R. China

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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