Third-order Nonlinear Neutral Differential Equations Research Articles

Asymptotic Behavior and Oscillation of Third-Order Nonlinear Neutral Differential Equations with Mixed Nonlinearities

In this paper, we investigate the asymptotic properties of third-order nonlinear neutral differential equations with mixed nonlinearities using the comparison principle. Our results not only vastly improve upon but also broadly generalize many previously known ones. Examples demonstrating the applicability and efficacy of our results are provided.

Oscillation criteria for third-order nonlinear neutral differential equations with distributed deviating arguments

In this paper, we consider the oscillation of a class of third-order nonlinear neutral differential equations with distributed deviating arguments by using comparison principles. The obtained criteria essentially extend and improve related results in the literature by removing some restrictive conditions, which can easily be extended to more general third-order differential equations. Examples are also given to illustrate the established results.

New Results for Kneser Solutions of Third-Order Nonlinear Neutral Differential Equations

In this paper, we consider a certain class of third-order nonlinear delay differential equations r w ″ α ′ v + q v x β ς v = 0 , for v ≥ v 0 , where w v = x v + p v x ϑ v . 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.

On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations

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

Oscillation of third-order neutral differential equations with damping and distributed delay

The present paper focuses on the oscillation of the third-order nonlinear neutral differential equations with damping and distributed delay. The oscillation of the third-order damped equations is often discussed by reducing the equations to the second-order ones. However, by applying the Riccati transformation and the integral averaging technique, we give an analytical method for the estimation of Riccati dynamic inequality to establish several oscillation criteria for the discussed equation, which show that any solution either oscillates or converges to zero. The results make significant improvement and extend the earlier works such as (Zhang et al. in Appl. Math. Lett. 25:1514–1519 2012). Finally, some examples are given to demonstrate the effectiveness of the obtained oscillation results.

Some New Oscillatory Behavior of Certain Third-Order Nonlinear Neutral Differential Equations of Mixed Type

By applying Riccati substitution techniques triply, we establish some new oscillation and asymptotic nature of solutions to the third-order nonlinear differential equations with mixed neutral type. We present many theorems and related examples in order to illustrate and substantiate the main theory.

Oscillatory and asymptotic behavior of a third-order nonlinear neutral differential equation

This paper discusses oscillatory and asymptotic properties of solutions of a class of third-order nonlinear neutral differential equations. Some new sufficient conditions for a solution of the equation to be either oscillatory or to converges to zero are presented. The results obtained can easily be extended to more general neutral differential equations as well as to neutral dynamic equations on time scales. Two examples are provided to illustrate the results.

Oscillation Criteria for Third-order Nonlinear Neutral Differential Equations with Distributed Deviating Arguments

Oscillation Criteria for Third-order Nonlinear Neutral Differential Equations with Distributed Deviating Arguments

Oscillation of third-order nonlinear neutral differential equations

We establish some new criteria for the oscillation and asymptotic behaviour of solutions of the third-order nonlinear neutral differential equation ( 1 p ( t ) ( 1 r ( t ) [ x ( t ) + a ( t ) x ( γ ( t ) ) ] ′ ) ′ ) ′ + q ( t ) f ( x ( δ ( t ) ) ) = 0 . Applications illustrating the results are given.

Asymptotic Properties of Solutions to Third-Order Nonlinear Neutral Differential Equations

The aim of this work is to discuss asymptotic properties of a class of third-order nonlinear neutral functional differential equations. The results obtained extend and improve some related known results. Two examples are given to illustrate the main results.

Oscillation criteria for a class of third-order nonlinear neutral differential equations

is investigated in this paper, where y(t) = x(t) + p(t)x(τ(t)), and α > 0 is any quotient of odd integers. Using a new method, we obtain some sufficient conditions for the oscillation of the above equation, and some known oscillation criteria be extended. An example is inserted to illustrate the result.