The nonlinear singular integral equation for ”self-energy” \(\Sigma\) (k,z) arising in Kirkpatrick’s mode-coupling theory of glass transition is analyzed without suppressing the k dependence. An equation that is equivalent to Kirkpatrick’s equation and suitable for high density is set up. Applicability of D. Lika’s generalization of the Newton- Kantorovich successive approximation [Functional analysis and approximate solutions of nonlinear equations (1975; Zbl 0312.47050)] is discussed. The possibility of solutions that cannot be found by iteration is pointed out.