Vol. 63, No. 2, 1976

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Asymptotic behavior of solutions of retarded differential difference equations

James C. Lillo

Vol. 63 (1976), No. 2, 431–444

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.

Mathematical Subject Classification
Primary: 34K15
Received: 28 May 1975
Published: 1 April 1976
James C. Lillo