Fourth-Order Emden–Fowler Neutral Differential Equations: Investigating Some Qualitative Properties of Solutions.

In this article, we investigate some of the qualitative properties of a class of fourth-order neutral differential equations. We start by obtaining new inequalities and relations between the solution and its corresponding function, as well as with its derivatives. The new relations allow us to improve the monotonic and asymptotic properties of the positive solutions of the studied equation. Then, using an improved approach, we establish new criteria that test the oscillation of all solutions. We also rely on the principle of symmetry between positive and negative solutions to obtain the new criteria. The paper provides illustrative examples that highlight the significance of our findings. [ABSTRACT FROM AUTHOR]