Linear functional differential equations with property A. (Q1406536)

The paper deals with oscillatory properties of the linear functional- differential equation \[ u^{(n)}(t)+ \sum^m_{i=1} \int^{\sigma_i(t)}_{\tau_i(t)} u(s)\,d_s r_i(s, t)= 0, \] where \(n\geq 2\), \(\tau_i(t)\leq \sigma_i(t)\), \(\tau_i(t)\to \infty\) for \(t\to\infty\) and the functions \(r_i\) are nondecreasing in the first argument and Lebesgue integrable in the second one. Conditions are found for all solutions \(u\) to be oscillatory when \(n\) is even, and either oscillatory or tending to zero when \(n\) is odd.