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On an almost periodic delay-differential system with almost periodic delays. (English) Zbl 0613.34062

The paper deals with a linear system of the form \[ (1)\quad \frac{dX(t)}{dt}=A(t)X(t)+\sum^{N}_{j=1}B_ j(t)X(t-\tau_ j(t)+F(t),\quad t\in R \] where \(A,B_ j\) \((j=1,2,...,N)\) are almost periodic (a.p.) \(n\times n\) matrices, F is an a.p. n-vector and \(\tau_ j\) \((j=1,2,...,N)\) are a.p. scalars. The author, using properties of a.p. functions and differential equations with a.p. coefficients and properties of matrix measures, derives sufficient conditions for the existence of a unique asymptotically stable a.p. solution of (1).
Reviewer: J.Ohriska

MSC:

34K20 Stability theory of functional-differential equations
34D20 Stability of solutions to ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
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