### Abstract

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

Original language | English |
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Pages (from-to) | 765-790 |

Number of pages | 26 |

Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |

Volume | 143 A |

Issue number | 4 |

DOIs | |

Publication status | Published - 2013 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Proceedings of the Royal Society of Edinburgh Section A: Mathematics*,

*143 A*(4), 765-790. https://doi.org/10.1017/S0308210511001752

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*Proceedings of the Royal Society of Edinburgh Section A: Mathematics*, vol. 143 A, no. 4, pp. 765-790. https://doi.org/10.1017/S0308210511001752

**On semiclassical states of a nonlinear Dirac equation.** / Ding, Y. H.; Lee, Cheng; Ruf, B.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On semiclassical states of a nonlinear Dirac equation

AU - Ding, Y. H.

AU - Lee, Cheng

AU - Ruf, B.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - We study the semiclassical limit of the least energy solutions to the nonlinear Dirac equation. We prove that the equation has least energy solutions for all Ä§ > 0 small, and, in addition, that the solutions converge in a certain sense to the least energy solution of the associated limit problem as Ä§ → 0.

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

UR - http://www.scopus.com/inward/record.url?scp=84880538482&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880538482&partnerID=8YFLogxK

U2 - 10.1017/S0308210511001752

DO - 10.1017/S0308210511001752

M3 - Article

AN - SCOPUS:84880538482

VL - 143 A

SP - 765

EP - 790

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 4

ER -