Nonlinear integral equation from the BCS gap equations of superconductivity

We present the proof of the existence and uniqueness of a positive nontrivial solution to the system of nonlinear integral equation arising from the model of anisotropic multiband BCS Gap Equations of superconductivity. Moreover, we will show that the critical temperature TcTc of the occurrence of superconductivity is determined through the determination of the first eigenvalue of the kernel function of the system.