Geodesic
On periodic solutions of systems of linear functional-differential equations
Archivum mathematicum, Tome 33 (1997) no. 3, pp. 197-212.

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This paper deals with the system of functional-differential equations \[ \frac{dx(t)}{dt}=p(x)(t)+q(t), \] where $p:C_\omega ({R}^n)\rightarrow L_\omega ({R}^n)$ is a linear bounded operator, $q\in L_\omega ({R}^n)$, $\omega >0$ and $C_\omega ({R}^n)$ and $L_\omega ({R}^n)$ are spaces of $n$-dimensional $\omega $-periodic vector functions with continuous and integrable on $[0,\omega ]$ components, respectively. Conditions which guarantee the existence of a unique $\omega $-periodic solution and continuous dependence of that solution on the right hand side of the system considered are established.
Classification : 34C25, 34K05, 34K13, 34K15
Keywords: linear functional-differential system; differential system with deviated argument; $\omega$-periodic solution 
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Kiguradze, Ivan; Půža, Bedřich. On periodic solutions of systems of linear functional-differential equations. Archivum mathematicum, Tome 33 (1997) no. 3, pp. 197-212. http://geodesic.mathdoc.fr/item/ARM_1997__33_3_a2/