A Survey on Sharp Oscillation Conditions of Differential Equations with Several Delays

In this paper, the state-of-the-art on the sharp oscillation conditions are presented. In particular, several sufficient oscillation conditions are presented, and it is shown that, under additional hypotheses dealing with slowly varying at infinity functions, some of the “liming” oscillation conditions can be essentially improved by replacing “liming” with “limp”. The importance of the slowly varying hypothesis and the essential improvement of the sufficient oscillation conditions are illustrated by example,