The objective in this work is to study oscillation criteria for second-order quasi-linear differential equations with an advanced argument. We establish new oscillation criteria using both the comparison technique with first-order advanced differential inequalities and the Riccati transformation. The established criteria improve, simplify and complement results that have been published recently in the literature. We illustrate the results by an example.

The purpose of this work is to study the oscillation criteria for generalized Emden–Fowler neutral differential equation. We establish new oscillation criteria using both the technique of comparison with first order delay equations and the technique of Riccati transformation. Our new criteria are interesting as they improve, simplify, and complement some results that have been published recently in the literature. Moreover, we present an illustrating example.

In this paper, we investigate the oscillatory behavior of solutions of second-order differential equations with a superlinear neutral term and a damping term in noncanonical forms. We do not place any additional conditions on the damping term. Therefore, our results apply to new classes of equations that were not covered by the previous criteria. According to symmetry between the negative and positive solutions of the studied equation, we present some new criteria that ensure the oscillation of all solutions by using the Riccati transformation and comparison method. We provide an example to illustrate our main results.

In this paper, we consider a certain class of third-order nonlinear delay differential equations ${\left(r{\left(w^{″}\right)}^{\alpha }\right)}^{\prime }\left(v\right)+q\left(v\right)x^{\beta }\left(\varsigma \left(v\right)\right)=0,$ for $v\ge v_0,$ where $w\left(v\right)=x\left(v\right)+p\left(v\right)x\left(\vartheta \left(v\right)\right)$ . We obtain new criteria for oscillation of all solutions of this nonlinear equation. Our results complement and improve some previous results in the literature. An example is considered to illustrate our main results.

In this paper, we are interested in studying the oscillation of differential equations with a damping term and distributed delay. We establish new criteria that guarantee the oscillation of the third-order differential equation in terms of oscillation of the second-order linear differential equation without a damping term. By using the Riccati transformation technique and the principle of comparison, we obtain new results on the oscillation for the studied equation. The results show significant improvement and extend the previous works. Symmetry contributes to determining the correct methods for solving neutral differential equations. Some examples are provided to show the significance of our results.

This paper is concerned with the oscillation and asymptotic behavior of certain third-order nonlinear delay differential equations with distributed deviating arguments. By establishing sufficient conditions for the nonexistence of Kneser solutions and existing oscillation results for the studied equation, we obtain new criteria which ensure that every solution oscillates by using the theory of comparison with first-order delay equations and the technique of Riccati transformation. Some examples are presented to illustrate the importance of main results.