Abstract New oscillation criteria for the second‐order Emden–Fowler delay differential equation with a sublinear neutral term are presented. An essential feature of our results is that studied ensured via only one condition. Furthermore, as opposed to by Agarwal et al. (Ann. Mat. Pura Appl. (4) 193 (2014), no. 6, 1861–1875), Li and Rogovchenko (Math. Nachr. 288 (2015), 10, 1150–1162; Monatsh. Math. 184 (2017), 3, 489–500), Xu (Monatsh. 150 (2007), 2, 157–171), new can be applied equations...

We study oscillatory behavior of a class second‐order neutral differential equations under the assumptions that allow applications to with both delayed and advanced arguments, not only. New theorems complement improve number results reported in literature. Illustrative examples are provided.

By using comparison principles, we analyze the asymptotic behavior of solutions to a class third-order nonlinear neutral differential equations. Due less restrictive assumptions on coefficients equation and deviating argument τ, our criteria improve number related results reported in literature.

New sufficient conditions for the oscillation of all solutions to a class third‐order Emden–Fowler differential equations with unbounded neutral coefficients are established. The criteria obtained essentially improve related results in literature. In particular, as opposed known results, new can distinguish different behaviors. Examples also provided illustrate results.

Abstract We study scalar advanced and delayed differential equations with piecewise constant generalized arguments, in short DEPCAG of mixed type, that is, the arguments are general step functions. It is shown argument deviation generates, under certain conditions, oscillations solutions, which an impossible phenomenon for corresponding equation without deviations. Criteria existence periodic solutions such discussed. New criteria extend improve related results reported literature. The...

The paper is devoted to the study of oscillation solutions a class second-order half-linear neutral differential equations with delayed arguments. New criteria are established, and they essentially improve well-known results reported in literature, including those for non-neutral equations. adopted approach refines classical Riccati transformation technique by taking into account such part overall impact delay that has been neglected earlier results. effectiveness obtained illustrated via examples.

Abstract In this note, we establish some oscillation criteria for certain higher-order quasi-linear neutral differential equation. These improve those results in the literature. Some examples are given to illustrate importance of our results. 2010 Mathematics Subject Classification 34C10; 34K11.

This paper is concerned with oscillation of a certain class second-order differential equations sublinear neutral term. Two criteria and two illustrative examples are included. In particular, the results obtained improve those reported in literature.

We study oscillatory behavior of a class fourth-order neutral differential equations with p-Laplacian like operator using the Riccati transformation and integral averaging technique. A Kamenev-type oscillation criterion is presented assuming that noncanonical case satisfied. This new theorem complements improves number results reported in literature. An illustrative example provided. MSC:34C10, 34K11.

We study the oscillatory behavior of differential equations with nonmonotone deviating arguments and nonnegative coefficients. New oscillation criteria, involving lim sup inf, are obtained based on an iterative method. Examples, numerically solved in MATLAB, given to illustrate applicability strength conditions over known ones.

We study asymptotic behavior of solutions to a class higher-order quasilinear neutral differential equations under the assumptions that allow applications even- and odd-order with delayed advanced arguments, as well functional more complex arguments may, for instance, alternate indefinitely between types. New theorems extend number results reported in literature. Illustrative examples are presented.

Abstract We obtain several oscillation criteria for a class of second-order nonlinear neutral differential equations. New theorems extend number related results reported in the literature and can be used cases where known fail to apply. Two illustrative examples are provided. MSC: 34K11.

The purpose of this paper is to examine oscillatory properties the third‐order neutral delay differential equation [ a ( t )( b x ) + p σ ))) ′ ] q τ )) = 0. Some and asymptotic criteria are presented. These improve complement those results in literature. Moreover, some examples given illustrate main results.