Semi-classical limits of ground states of a nonlinear Dirac equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:252

Article

Ding, Yanheng^1,2  Liu, Xiaoying³ 

[1] Chinese Acad Sci, AMSS, Inst Math, Beijing 100190, Peoples R China

[2] Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China

[3] Xuzhou Normal Univ, Dept Math, Xuzhou 221116, Jiangsu, Peoples R China

关键词: Nonlinear Dirac equation;    Semi-classical states;    Concentration;   

DOI  :  10.1016/j.jde.2012.01.023

来源: Elsevier

【 摘 要 】

We study the semi-classical states of the following nonlinear Dirac equation [GRAPHICS] for x is an element of R-3 where the nonlinearity is of superlinear and subcritical growth as vertical bar w vertical bar -> infinity. The Dirac operator is unbounded from below and above so the associate energy functional is strongly indefinite. We develop an argument to establish the existence of least energy solutions for h small. We also describe the concentration phenomena of the solutions as h -> 0. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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