Some remarks on the asymptotic behavior of a nonautonomous,nonlinear functional differential equation

The asymptotic behavior of the abstract nonautonomous, nonlinear functional differential equation $\text{x}\text{?}\text{(t) = f(t, x(t)) + g(t, x}{}_{\mathrm{t}}\text{), x}{}_{\mathrm{s}}\text{= ?}$ is considered. Estimates on the growth of solutions are given and these estimates are shown to be the best possible.