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On the Bardeen-Cooper-Schrieffer integral equation in the theory of superconductivity. (English) Zbl 0729.45009
The paper deals with the study of the Bardeen-Cooper-Schrieffer integral equation which appears in the theory of superconductivity. Assuming the positiveness of the kernel of that equation it is shown that there exists a unique finite transition temperature \(T_ c\) such that if \(T<T_ c\) then the equation in question possesses a positive solution. Moreover, it is proved that such a solution may be approximated by a sequence of solutions of the Bardeen-Cooper-Schrieffer equation restricted to bounded domains.

MSC:
45G10 Other nonlinear integral equations
45M20 Positive solutions of integral equations
82D55 Statistical mechanical studies of superconductors
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