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This paper focuses on studying the oscillatory properties of a distinctive class of second-order advanced differential equations with distributed deviating arguments in a noncanonical case. Utilizing the Riccati method and the comparison method with first-order equations, in addition to other analytical methods, we have established criteria to test whether the solutions of the studied equation exhibit oscillatory behavior. To verify the validity of the results we obtained and determine their applicability, we present some examples to confirm the strength and accuracy of our proposed criteria. [ABSTRACT FROM AUTHOR]

In this paper, we address the study of the oscillatory properties of the solutions of a class of third-order delay differential equations. The primary objective of this study is to provide new relationships that can be employed to obtain criteria for excluding increasing positive solutions and decreasing positive solutions so that the resulting criteria are easier to apply than other criteria that have appeared in the literature. We have obtained new oscillation criteria that hold up more robustly upon application. Some examples are presented to illustrate the significance of our main findings. [ABSTRACT FROM AUTHOR]

This paper focuses on studying certain oscillatory properties of a new class of half-linear second-order differential equations with an advanced argument in a non-canonical case. By employing some new relations between the solution and its higher derivatives and taking into account the symmetry of positive and negative solutions, we have introduced new criteria to test whether all solutions of the studied equation exhibit oscillatory behavior. Our study aims to expand and enhance previous results, helping to understand these properties in the specified context. The results obtained are confirmed and clarified through an example involving Euler-type equations. [ABSTRACT FROM AUTHOR]

In the current paper, we aim to study the oscillatory behavior of a new class of third-order differential equations. In the present study, we are interested in a better understanding of the relationships between the solutions and their derivatives. The recursive nature of these relationships enables us to obtain new criteria that ensure the oscillation of all solutions of the studied equation. In comparison with previous studies, our results are more general and include models in a wider range of applications. Furthermore, our findings are also significant because no additional restrictive conditions are required. The presented examples illustrate the significance of the results. [ABSTRACT FROM AUTHOR]

In this paper, we consider two universal higher order dynamic equations with several delay functions. We will establish two oscillatory criteria of the first equation and a sufficient and necessary condition for the second equation with a nonoscillatory solution by employing fixed point theorem. [ABSTRACT FROM AUTHOR]

This study is connected with the nonoscillatory and oscillatory behaviour to the solutions of nonlinear neutral impulsive systems with forcing term which is studied for various ranges of of the neutral coefficient. Furthermore, sufficient conditions are obtained for the existence of positive bounded solutions of the impulsive system. The mentioned example shows the feasibility and efficiency of the main results. [ABSTRACT FROM AUTHOR]

Oscillation and symmetry play an important role in many applications such as engineering, physics, medicine, and vibration in flight. In this work, we obtain sufficient and necessary conditions for the oscillation of the solutions to a second-order differential equation with impulses and mixed delays when the neutral coefficient lies within [ 0 , 1) . Furthermore, an examination of the validity of the proposed criteria has been demonstrated via particular examples. [ABSTRACT FROM AUTHOR]

The oscillation of differential equations plays an important role in many applications in physics, biology and engineering. The symmetry helps to deciding the right way to study oscillatory behavior of solutions of this equations. The purpose of this article is to establish new oscillatory properties which describe both the necessary and sufficient conditions for a class of nonlinear second-order differential equations with neutral term and mixed delays of the form p (ι) w ′ (ι) α ′ + r (ι) u β (ν (ι)) = 0 , ι ≥ ι 0 where w (ι) = u (ι) + q (ι) u (ζ (ι)). Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples. [ABSTRACT FROM AUTHOR]

In this work, we present some new sufficient conditions for the oscillation of a class of second-order neutral delay differential equation. Our oscillation results, complement, simplify and improve recent results on oscillation theory of this type of non-linear neutral differential equations that appear in the literature. An example is provided to illustrate the value of the main results. [ABSTRACT FROM AUTHOR]