The Bethe--Salpeter equation applies to all kinematic region of the Bethe--Salpeter amplitude. Consequently it determines the amplitudes where the functions are not continuous. Such singularities are usually located when the constituent momentum is timelike, which are not directly accessible from Euclidean-space solutions of this equation. Instead one develop methods to solve these type of integral equations directly in the timelike region. In the case of scalar bound states through a scalar-particle exchange in the rainbow-ladder truncation, the Bethe--Salpeter equation in the Minkowski space can be solved with the assistance of Nakanishi integral representation.