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.
- AMS subject classifications (1980): 81J05, 82A25, 45G05
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics