Addendum to “The solution to the BCS gap equation and the second-order phase transition in superconductivity” [J. Math. Anal. Appl. 383 (2011) 353–364]

This is an addendum to my preceding paper Watanabe (2011) [10]. We show that the solution to the BCS gap equation in superconductivity is continuous with respect to both the temperature TT and the energy xx under a certain condition when the potential U(⋅,⋅)U(⋅,⋅) is not a constant. To this end we regard the BCS gap equation as a nonlinear integral equation on a Banach space consisting of continuous functions of both TT and xx.