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On periodic solutions to systems of linear functional-differential equations. (English) Zbl 0914.34062
Let $$\omega$$ be a positive number, $$C_{\omega } (\mathbb{R}^n)$$ (resp. $$L_{\omega } (\mathbb{R}^n)$$) be the space of $$n$$-dimensional $$\omega$$-periodic continuous (resp. integrable on $$[0,\omega ]$$) vector functions. The authors consider the system of functional-differential equations $x' (t) - p(x)(t) = q(t),$ where $$p:C_{\omega } (\mathbb{R}^n)\rightarrow L_{\omega }(\mathbb{R}^n)$$ is a linear bounded operator and $$q\in L_{\omega } (\mathbb{R}^n)$$. New 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 are given.

##### MSC:
 34K05 General theory of functional-differential equations 34K13 Periodic solutions to functional-differential equations 34K10 Boundary value problems for functional-differential equations 34C25 Periodic solutions to ordinary differential equations
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