On Linear Differential Equations with Retarded Arguments

On a linear differential system of neutral type

“…Here the purpose is to decompose the space of initial functions into classes in such a way that, for each class, the space of corresponding solutions is of finite dimension. From this point of view some results of this paper improve analogous results in [7] and [4]. More precisely, in this paper we consider the differential system…”

“…As in [7], we can prove the following proposition. PROPOSITION As an application of the above we give the next corollary, which improves Theorem 1 in [4] for the linear case.…”

“…For more details we mention the book of Hale [3,Chapters 7 and 8]. Recently Karakostas [5] and Staikos and Tsamatos [7] proved that an evolution operator, analogous to the evolution operator of linear differential systems, can be defined for some particular case of solutions of linear differential systems with retarded arguments. This expression of solutions is closely related to the dimension of the space of such solutions.…”

“…Therefore, a decomposition of the space of solutions of a differential system with [2] Linear differential system 227 deviating arguments into finite dimensional subspaces provides a nice approach to this problem. For a more detailed treatment in that direction, we refer the reader to Norkin [6] and to Staikos and Tsamatos [7]. Here the purpose is to decompose the space of initial functions into classes in such a way that, for each class, the space of corresponding solutions is of finite dimension.…”

“…Therefore, a decomposition of the space of solutions of a differential system with deviating arguments into finite dimensional subspaces provides a nice approach to this problem. For a more detailed treatment in that direction, we refer the reader to Norkin [6] and to Staikos and Tsamatos [7].…”