THE EVOLUTION OPERATOR APPROACH TO FUNCTIONAL-DIFFERENTIAL EQUATIONS WITH DELAY

The nonlinear nonautonomous functional differential equation x(t) is-an-element-of B(t) x(t) + F(t, x(t)), t greater-than-or-equal-to s, x(s) = phi, is considered. The representation of the solution to this equation via the associated evolution operator is extended from the single-valued case to the general case of multivalued operators B(t).