 $$\begin{aligned} -\frac{0}{(0\pi)^0}\sum_{\beta}\oint_{FS} dk'_{\Vert}\frac{V^{\alpha\beta}(\bm{k,k'})}{v^{\beta}_{F}(\bm{k'})} \Delta_{\beta}(\bm{k'})=\lambda \Delta_{\alpha}(\bm{k}).\label{eigenvalue_Tc0}\end{aligned}$$ 