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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.

45G10 Other nonlinear integral equations
45M20 Positive solutions of integral equations
82D55 Statistical mechanical studies of superconductors
Full Text: DOI
[1] Bardeen J., Cooper L. N., and Schrieffer J. L., Theory of superconductivity, Phys. Rev. 108, 1175-1204 (1957). · Zbl 0090.45401 · doi:10.1103/PhysRev.108.1175
[2] Billard P. and Fano G., An existence proof for the gap equation in the superconductivity theory, Comm. Math. Phys. 10, 274-279 (1968). · Zbl 0164.57002
[3] Ginzburg V. L. and Landau L. D., On the theory of superconductivity, in D. terHaar (ed), Collected Papers of L.D. Landau, Pergamon, New York, 1965, pp. 546-568.
[4] Gorkov L. P., Microscopic derivation of the Ginzburg-Landau equations in the theory of superconductivity, Soviet Phys. JETP 9, 1364-1367 (1959). · Zbl 0088.45602
[5] Hugenholtz N. M., Quantum theory of many-body systems, Rep. Progr. Phys. 28, 201-247 (1965). · Zbl 0184.54801 · doi:10.1088/0034-4885/28/1/307
[6] Odeh F., An existence theorem for the BCS integral equation, IBM J. Res. Develop. 8, 187-188 (1964). · doi:10.1147/rd.82.0187
[7] van Hemmen L., Linear fermion systems, molecular field models, and the KMS condition, Fortschr. Phys. 26, 379-439 (1978).
[8] Vansevenant A., The gap equation in superconductivity theory, Physica D 17, 339-344 (1985). · doi:10.1016/0167-2789(85)90217-9
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