
Minimax Theory and its Applications 06 (2021), No. 1, 025060 Copyright Heldermann Verlag 2021 Concentration of SemiClassical States for Nonlinear Dirac Equations of SpaceDimension 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 semiclassical approximation of a massive Dirac equation in spacedimension n ≥ 2 with some general nonlinear selfcoupling. We prove that there exists a family of ground states of the semiclassical 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, semiclassical states, concentration. MSC: 35B25, 35Q40, 49J35. [ Fulltextpdf (239 KB)] for subscribers only. 