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

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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.

Original languageEnglish (US)
Pages (from-to)27-37
Number of pages11
JournalLetters in Mathematical Physics
Issue number1
StatePublished - May 1991


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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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