SOLUTIONS OF SELF-DIFFERENTIAL FUNCTIONAL EQUATIONS.

The system of functional differential equations (1) has a continuously differentiable solution for every value of the parameter a. The boundary values and a are related with d(2 - a) = c(2 + a). When a ∈ S where S= {22n+1 :n=1,2,3, …}, the system (1) has infinitely many solutions with boundary values c= 0 and d = O. For all other values of a, the system (1) has a unique solution. F' (x) = aF(2x) if 0 ≤ x ≤ ½ F' (x) = aF(2-2x) if ½ x ≤ 1 F(0) = c, F(1) = d. [ABSTRACT FROM AUTHOR]