Positivity of solutions to boundary value problems for infinite functional differential systems

In this paper the problems of unique solvability of boundary value problems for infinite functional differential systems and positivity of their solutions are reduced to analysis of scalar functional equations in the space of measurable essentially bounded functions y : [ 0 , + ∞ ) → ( − ∞ , + ∞ ) . Efficient tests of the solvability and the positivity are obtained.