Oscillations of certain delay integro-differential equations (Q1969402)

The authors study the existence and nonexistence of componentwise sign-definite solutions to the delay integro-differential system \[ x'_i(t) + \sum_{j=1}^n\int_0^t D_{i,j}(t-s)x_j(s-\tau) ds = 0, \quad i = 1,2,\ldots,n,\quad t \geq 0, \tag \(*\) \] and the nonhomogeneous version of this system, where the zeros on the right-hand side are replaced by \(f_i(t)\). Most of the theorems are of comparison type: the behavior of the solutions to (\(*\)) are compared to the behavior of the solutions to the same equation with \(D_{i,j}\) replaced by some other related functions \(E_{i,j}\).