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On semiclassical states of a nonlinear Dirac equation

Published online by Cambridge University Press:  17 July 2013

Y. H. Ding
Institute of Mathematics, Academy of Mathematics and Systems Science and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China (
C. Lee
Department of Mathematics, National Changhua University of Education, Changhua 500, Taiwan, Republic of China
B. Ruf
Dipartimento di Matematica, Universitá degli Studi di Milano, Via Cesare Saldini 50, 20133 Milano, Italy (


We study the semiclassical limit of the least energy solutions to the nonlinear Dirac equation for x ∈ ℝ3. We prove that the equation has least energy solutions for all ħ > 0 small, and, in addition, that the solutions converge in a certain sense to the least energy solution of the associated limit problem as ħ → 0.

Research Article
Copyright © Royal Society of Edinburgh 2013 

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