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On linear differential equations with retarded arguments. (English) Zbl 0562.34051

The idea of using fixed points of the lag in a linear differential equation with retarded argument, was proposed by G. Karakostas [Boll. Unione Mat. Ital., V. Ser. A 17, 428-435 (1980; Zbl 0455.34047)] and is widely applied here to a system of the form \(\dot x(t)=\sum^{k}_{i=1}A_ i(t)x[\sigma_ i(t)]+b(t).\) The authors discuss solutions with initial value \((\bar t,\xi)\) where \(\bar t\) is any point such that \(\sigma_ i(\bar t)=\bar t\), \(i=1,2,...,k\) and examine various properties (such as representation, dimension etc.) which are analogous to those of ordinary differential equations. By succeeding a representation of such solutions it is also shown how one can get oscillation and asymptotic equilibrium results.
Reviewer: G.Karakostas

MSC:

34K05 General theory of functional-differential equations
34A30 Linear ordinary differential equations and systems

Citations:

Zbl 0455.34047
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References:

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