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On periodic solutions of first order linear functional differential equations. (English) Zbl 1008.34062

Here, the functional-differential equation \[ u'(t)= l(u)(t)+ g(t)\tag{1} \] is considered, where \(l\) is a linear bounded operator from the space \(C_\omega(\mathbb{R})\) of continuous \(\omega\)-periodic functions to the space \(L_\omega(\mathbb{R})\) of \(\omega\)-periodic Lebesgue integrable functions and \(g\in L_\omega(\mathbb{R})\). New optimal sufficient conditions are established for the existence of a unique \(\omega\)-periodic solution to (1).

MSC:

34K13 Periodic solutions to functional-differential equations
34K06 Linear functional-differential equations
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