The asymptotic behavior of the
solutions of nonautonomous n-th order linear retarded differential difference
equations is studied in this paper. It is shown that if the coefficients satisfy certain
restrictions, then for any real K there exists a finite dimensional subspace F(K) of
the solution space having the following property. For any solution x of the equation
one has for all t > 0 that x(t) = xK(t) + xr(t) where xk belongs to F(K) and
xr(t) = 0(exp(−Kt)) as t →∞. As in the author’s earlier papers, considering the
periodic and almost periodic cases, the spaces F(K) are obtained by treating the
nonautonomous equation as a perturbation of an n-th order autonomous
equation.
