Semi-classical ground states concentrating on the nonlinear potential for a Dirac equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:249

Article

Ding, Yanheng^1,2 

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

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

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

DOI  :  10.1016/j.jde.2010.03.022

来源: Elsevier

【 摘 要 】

We study the semi-classical limit of the least energy solutions to the nonlinear Dirac equation -i epsilon Sigma(3)(k=1)alpha(k)partial derivative(k) + a beta u = P(x)vertical bar u vertical bar(p-2)u for x is an element of R-3. Since the Dirac operator is unbounded from below and above, the associate energy functional is strongly indefinite, and since the problem is considered in the global space R-3, the Palais-Smale condition is not satisfied. New phenomena and mathematical interests arise in the use of the calculus of variations. We prove that the equation has the least energy solutions for all epsilon > 0 small, and additionally these solutions converge to the least energy solutions of the associate limit problem and concentrate to the maxima of the nonlinear potential P(x) in certain sense as epsilon -> 0. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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