Unique solvability and constancy of sign of the Green function of a periodic boundary value problem for a linear equation with deviating argument (Q1901914)

The author considers the periodic boundary value problem for a linear equation with deviating argument of the type (1) \(x^{(n)} (t) = \int^b_a x(s) d_s r(t,s) + f(t)\), \(t \in [a,b]\), \(x^{(i)} (a) = x^{(i)} (b)\), \(i = 0, \dots, n - 1\). She obtains a necessary and sufficient condition for unique solvability of (1) as well as certain conditions for the Green function of (1) to have constant sign.