### Abstract

For a domain Ω in the Euclidean space Rd (d = 2, 3) existence of weak solutions for both interior and exterior Dirichlet boundary value problems of the Ginzburg-Landau equations are established without any restriction on the range of the coupling constant λ, the size of Ω, or the boundary data. For the critical choice λ = 1, we prove the existence of confined multivortices in a bounded domain by a constructive monotone iteration method.

Original language | English (US) |
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Pages (from-to) | 355-365 |

Number of pages | 11 |

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

Volume | 114 |

Issue number | 3-4 |

DOIs | |

State | Published - 1990 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Boundary value problems of the Ginzburg-Landau equations.** / Yang, Yisong.

Research output: Contribution to journal › Article

*Proceedings of the Royal Society of Edinburgh Section A: Mathematics*, vol. 114, no. 3-4, pp. 355-365. https://doi.org/10.1017/S0308210500024471

}

TY - JOUR

T1 - Boundary value problems of the Ginzburg-Landau equations

AU - Yang, Yisong

PY - 1990

Y1 - 1990

N2 - For a domain Ω in the Euclidean space Rd (d = 2, 3) existence of weak solutions for both interior and exterior Dirichlet boundary value problems of the Ginzburg-Landau equations are established without any restriction on the range of the coupling constant λ, the size of Ω, or the boundary data. For the critical choice λ = 1, we prove the existence of confined multivortices in a bounded domain by a constructive monotone iteration method.

AB - For a domain Ω in the Euclidean space Rd (d = 2, 3) existence of weak solutions for both interior and exterior Dirichlet boundary value problems of the Ginzburg-Landau equations are established without any restriction on the range of the coupling constant λ, the size of Ω, or the boundary data. For the critical choice λ = 1, we prove the existence of confined multivortices in a bounded domain by a constructive monotone iteration method.

UR - http://www.scopus.com/inward/record.url?scp=84974270184&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84974270184&partnerID=8YFLogxK

U2 - 10.1017/S0308210500024471

DO - 10.1017/S0308210500024471

M3 - Article

VL - 114

SP - 355

EP - 365

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 - 3-4

ER -