### Abstract

The Bardeen-Cooper-Schrieffer integral equation with a positive kernel is studied in full generality. It is shown that, there exists a unique finite transition temperature, T_{c}so that, if T<T_{c},the equation possesses a positive solution, representing the onset of the superconducting phase, while if T>T_{c},the only solution of the equation is the trivial one, indicating the occurrence of the normal phase. Moreover, it is demonstrated that such a positive solution may be approximated by a sequence of solutions of the equation restricted on bounded domains. This latter result provides a useful computational scheme for the problem.

Original language | English (US) |
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Pages (from-to) | 27-37 |

Number of pages | 11 |

Journal | Letters in Mathematical Physics |

Volume | 22 |

Issue number | 1 |

DOIs | |

State | Published - May 1991 |

### Fingerprint

### Keywords

- AMS subject classifications (1980): 81J05, 82A25, 45G05

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

**On the Bardeen-Cooper-Schrieffer integral equation in the theory of superconductivity.** / Yang, Yisong.

Research output: Contribution to journal › Article

*Letters in Mathematical Physics*, vol. 22, no. 1, pp. 27-37. https://doi.org/10.1007/BF00400375

}

TY - JOUR

T1 - On the Bardeen-Cooper-Schrieffer integral equation in the theory of superconductivity

AU - Yang, Yisong

PY - 1991/5

Y1 - 1991/5

N2 - The Bardeen-Cooper-Schrieffer integral equation with a positive kernel is studied in full generality. It is shown that, there exists a unique finite transition temperature, Tcso that, if T<Tc,the equation possesses a positive solution, representing the onset of the superconducting phase, while if T>Tc,the only solution of the equation is the trivial one, indicating the occurrence of the normal phase. Moreover, it is demonstrated that such a positive solution may be approximated by a sequence of solutions of the equation restricted on bounded domains. This latter result provides a useful computational scheme for the problem.

AB - The Bardeen-Cooper-Schrieffer integral equation with a positive kernel is studied in full generality. It is shown that, there exists a unique finite transition temperature, Tcso that, if T<Tc,the equation possesses a positive solution, representing the onset of the superconducting phase, while if T>Tc,the only solution of the equation is the trivial one, indicating the occurrence of the normal phase. Moreover, it is demonstrated that such a positive solution may be approximated by a sequence of solutions of the equation restricted on bounded domains. This latter result provides a useful computational scheme for the problem.

KW - AMS subject classifications (1980): 81J05, 82A25, 45G05

UR - http://www.scopus.com/inward/record.url?scp=0002359313&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002359313&partnerID=8YFLogxK

U2 - 10.1007/BF00400375

DO - 10.1007/BF00400375

M3 - Article

AN - SCOPUS:0002359313

VL - 22

SP - 27

EP - 37

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 1

ER -