| Abstract: | Summary The objective of this paper is to give necessary and sufficient conditions for the existence of periodic solutions of coupled
systems of differential-difference and difference equations. By differentiating the difference equation, we obtain a system
of neutral differential-difference equations and we get the original problem by putting a side condition on the neutral equation;
that is, by restricting the initial data to lie on certain manifold in the space of all initial data. This allows us to treat
the problem using the methods of neutral functional differential equations. In8], Hale and Martinez-Amore exploited a certain change of variables to obtain some results on the stability of this systems.
In Section 2, we summarize those ideas. The effect of the side condition is reflected in the variation of constants formula
in Section 3. In this section, the variation of constants formula is decomposed via eigenspaces. In Section 4, we give a theorem
on the Fredholm alternative for periodic solutions which is basic to the application of the usual theory to perturbed linear
problems. I want to express my most deep gratitude to Professor J. K. Hale for his advice and suggestions which led to considerable
improvements of this paper.
Entrata in Redazione l'8 marzo 1978.
Research was supported in the form of Grant from the Program of Cultural Exchange between the United States and Spain. |
