In this paper we consider the one dimensional Dirac system
where αk(x) < 0, λ is a complex spectral parameter, and the remaining coefficients are suitably smooth and real valued. We regard (1.1) as regular at x = a but singular at x = b; in Section 4 we extend our result to problems having two singular endpoints.
Equation (1.1) arises from the three dimensional Dirac equation with spherically symmetric potential, following a separation of variables. For the choices p(x) = k/x, αk(x) = 1,p
2(x) = (z/x) + c, p
1(x) = (z/x) – c, and appropriate values of the constants, (1.1) is the radial wave equation in relativistic quantum mechanics for a particle in a field of potential V = z/x . Such an equation was studied by Kalf  in the context of limit point-limit circle criteria, which is one of the matters we consider here.