On the Cauchy Singular Problem for Systems of Functional Differential Equations

satisfies the condition f ρ ∈ Lloc(]a, b]; R). In regular case where f ρ ∈ L([a, b]; R) for any ρ > 0, problem (1), (2) is investigated in detail (see, e.g., [1]–[4], [9], [10] and the references therein). We are, in the main, interested in the case when f ρ is nonintegrable on [a, b], having singularity at t = a. In this case, the problem (1), (2) is singular one. The methods of investigation of the singular problem (1), (2) in the case, when f is either the Nemytskii or evolution operator, have been developed in [5]–[7], [11]–[15]. Below, the problem (1), (2) will be investigated without an assumption that f is evolutionary. We will use the following notation. R n is the space of vectors x = (x1, . . . , xn) with real components x1, . . . , xn and the norm ‖x‖ = n