*(English)*Zbl 0939.34062

The authors investigate oscillatory properties of solutions to the $n$th-order linear differential equation

where $p:{\mathbb{R}}_{+}\to \mathbb{R}$ is a locally integrable function of constant sign and $\tau :{\mathbb{R}}_{+}\to \mathbb{R}$ is a continuous nondecreasing function such that $\tau \left(t\right)\to \infty $ as $t\to \infty $. Equation (1) is studied as an ordinary differential equation ($\tau \left(t\right)\equiv t$) as well as a functional-differential equation in both the delayed case ($\tau \left(t\right)\le t$) and the advanced case ($\tau \left(t\right)\ge t$).

In a series of statements some sufficient conditions for equation (1) to have property $A$ or property $B$ are established. Moreover, comparisons with known results are given.

##### MSC:

34K11 | Oscillation theory of functional-differential equations |

34C10 | Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory |