In this article, we study a class of non-linear neutral delay differential equations of third order. We first prove criteria for non-existence of non-Kneser solutions, and criteria for non-existence of Kneser solutions. We then use these results to provide criteria for the under study differential equations to ensure that all its solutions are oscillatory. An example is given that illustrates our theory.

In this study, we establish new sufficient conditions for oscillation of solutions of second-order neutral differential equations with distributed deviating arguments. By employing a refinement of the Riccati transformations and comparison principles, we obtain new oscillation criteria that complement and improve some results reported in the literature. Examples are provided to illustrate the main results.

In this work, new oscillation criteria are established for a second-order differential equation with several sublinear neutral terms and in the canonical case. To determine the oscillation conditions, we followed the Riccati approach and also compared the studied equation with a first-order delay equation. Obtaining the oscillation conditions required deducing some new relationships linking the solution to the corresponding function as well as its derivatives. The paper addresses some interesting analytical points in the study of the oscillation of equations with several sublinear neutral terms. These new findings complement some well-known findings in the literature. Furthermore, an example is provided to show the importance of the results.

In this paper, we derive new properties for the decreasing positive solutions of half-linear delay differential equations of even order. The positive-decreasing solutions have a great influence on the study of qualitative properties, which include oscillation, convergence, etc.; therefore, we take care of finding sufficient conditions to exclude these solutions. In addition, we present new criteria for testing the oscillation of the studied equation.

In this paper, we investigate the oscillatory properties of fourth-order neutral delay differential equation solutions in the canonical situation. To our knowledge, this equation has received minimal research. We prove new improved features and relationships for the solution and the accompanying function. Based on these relationships, oscillation theorems were developed that guarantee oscillation of all solutions to the considered equation. The comparison principle used in our results is one of the most significant methods for investigating the oscillatory behavior of delay differential equations. The findings of our study extend and develop a number of previous findings in the literature.