Dependence of Tc on electronic density of states

From the Eliashberg gap equations generalized to include approximately an energy dependence in the electron density of states N(ε) we compute the functional derivative of the critical temperature T_c with N(ε). It is found to be a rapidly decreasing function of the increasing energy away from the Fermi energy. In an appropriate limit, a comparison with the predictions of the McMillan equation shows that it is inadequate in a study of δT_c/δN(ε).