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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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