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On semiclassical states of a nonlinear Dirac equation

Published online by Cambridge University Press:  17 July 2013

Y. H. Ding
Affiliation:
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 (dingyh@math.ac.cn)
C. Lee
Affiliation:
Department of Mathematics, National Changhua University of Education, Changhua 500, Taiwan, Republic of China
B. Ruf
Affiliation:
Dipartimento di Matematica, Universitá degli Studi di Milano, Via Cesare Saldini 50, 20133 Milano, Italy (bernhard.ruf@unimi.it)

Abstract

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.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2013 

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