On periodic solutions of first order linear functional differential equations (Q1599957)

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).