On the Monotonic and Asymptotic Properties of Positive Solutions to Third-Order Neutral Differential Equations and Their Effect on Oscillation Criteria

The monotonic properties of positive solutions to functional differential equations of the third order are examined in this paper. It is generally known that by optimizing the relationships between a solution and its corresponding function, as well as its derivatives, one can improve the oscillation criterion for neutral differential equations. Based on this, we obtain new relationships and inequalities and test their effect on the oscillation parameters of the studied equation. To obtain the oscillation parameters, we used Riccati techniques and comparison with lower-order equations. Finally, the progress achieved in oscillation theory for third-order equations was measured by comparing our results with previous relevant results.