General conditions are obtained for the unique solvability of a non-local boundary value problem for systems of linear functional differential equations.

The problem on solutions with specified growth for linear functional differential equations with negative coefficients is treated by using two-sided monotone iterations. New theorems on the existence and localisation of such solutions are established.

Abstract. We obtain general conditions su‰cient for the solvability of a singular Cauchy problem for functional di¤erential equations with non-increasing nonlinearities.

We obtain new conditions under which a system of linear functional differential equations with singular coefficients has a unique solution possessing a given initial value and satisfying a certain growth restriction.