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Nonlinear integral equation from the BCS gap equations of superconductivity. (English) Zbl 1183.82097
The main result of the present paper establishes that the critical temperature \(T_c\) of the occurence of superconductivity is determined by the the first eigenvalue of the kernel function in the context of the Markowitz-Kadanoff model. The results developed in the present paper show that the determination of the critical temperature may be reduced to a singleton equation. The proofs rely on elementary monotonicity techniques.

MSC:
82D55 Statistical mechanical studies of superconductors
45G15 Systems of nonlinear integral equations
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