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.
@article{107611,
author = {Ivan Kiguradze and Bed\v rich P\r u\v za},
title = {On periodic solutions of systems of linear functional-differential equations},
journal = {Archivum Mathematicum},
volume = {033},
year = {1997},
pages = {197-212},
zbl = {0914.34062},
mrnumber = {1478773},
language = {en},
url = {http://dml.mathdoc.fr/item/107611}
}
Kiguradze, Ivan; Půža, Bedřich. On periodic solutions of systems of linear functional-differential equations. Archivum Mathematicum, Tome 033 (1997) pp. 197-212. http://gdmltest.u-ga.fr/item/107611/
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