Third-order Neutral Delay Differential Equations Research Articles

Existence and uniqueness criterion of a periodic solution for a third-order neutral differential equation with multiple delay

In this paper, we study the existence and uniqueness of a periodic solution for a third-order neutral delay differential equation (NDDE) by applying Mawhin’s continuation theorem of coincidence degree and analysis techniques. An illustrative example is given as an application to support our results. To confirm the accuracy of our results, we also present a plot of the behavior of the periodic solution.

Periodic behaviour of solution for a kind of third-order neutral delay differential equation

Periodic behaviour of solution for a kind of third-order neutral delay differential equation

Third-Order Neutral Delay Differential Equations: New Iterative Criteria for Oscillation

This study is aimed at developing new criteria of the iterative nature to test the oscillation of neutral delay differential equations of third order. First, we obtain a new criterion for the nonexistence of the so-called Kneser solutions, using an iterative technique. Further, we use several methods to obtain different criteria, so that a larger area of the models can be covered. The examples provided strongly support the importance of the new results.

Oscillation Criteria for a Class of Third-Order Damped Neutral Differential Equations

In this paper, we study the asymptotic and oscillatory properties of a certain class of third-order neutral delay differential equations with middle term. We obtain new characterizations of oscillation of the third-order neutral equation in terms of oscillation of a related, well-studied, second-order linear equation without damping. An Example is provided to illustrate the main results.

Oscillatory and asymptotic behavior of third-order neutral delay differential equations with distributed deviating arguments

This paper examines the oscillatory and asymptotic properties of a class of third-order neutral delay differential equations with distributed deviating arguments. A series of new oscillation criteria are presented under some more relaxed conditions by using the Riccati transformation technique. The results obtained here improve and complement that in the literature. At last, two examples are provided to illustrate the main results.

Oscillatory Properties of Third-Order Neutral Delay Differential Equations with Noncanonical Operators

In the paper, we study the oscillatory and asymptotic properties of solutions to a class of third-order linear neutral delay differential equations with noncanonical operators. Via the application of comparison principles with associated first and second-order delay differential inequalities, we offer new criteria for the oscillation of all solutions to a given differential equation. Our technique essentially simplifies the process of investigation and reduces the number of conditions required in previously known results. The strength of the newly obtained results is illustrated on the Euler type equations.

Oscillatory behavior of third-order neutral delay differential equations with distributed deviating arguments

The main contribution of this paper is to establish some new criteria, which ensure that every solution of third-order neutral delay differential equations with distributed deviating arguments is either oscillatory or tends to zero. The obtained theorems extend and improve several known results in the literature. Two examples are provided to illustrate the main results.

Stability and Square Integrability of Solutions to third order Neutral Delay Differential Equations

Abstract In this paper, sufficient conditions to guarantee the square integrability of all solutions and the asymptotic stability of the zero solution of a non-autonomous third-order neutral delay differential equation are established. An example is given to illustrate the main results.

On nonexistence of Kneser solutions of third-order neutral delay differential equations

The aim of this paper is to complement existing oscillation results for third-order neutral delay differential equations by establishing sufficient conditions for nonexistence of so-called Kneser solutions. Combining newly obtained results with existing ones, we attain oscillation of all solutions of the studied equations.

Oscillation results for third order nonlinear mixed neutral differential equations

Abstract In this paper, the authors study oscillatory and asymptotic behavior of solutions of a class of nonlinear third order neutral differential equations with positive and negative coefficients of the form (E) ( a ( t ) ( b ( t ) ( y ( t ) + p ( t ) y ( σ ( t ) ) ) ′ ) ′ ) ′ + q ( t ) G ( y ( α ( t ) ) ) − h ( t ) H ( y ( β ( t ) ) ) = 0 $$\begin{equation*}(a(t)(b(t)(y(t)+p(t)y(\sigma(t)))^{\prime})^{\prime})^{\prime} +q(t)G(y(\alpha(t)))-h(t)H(y(\beta(t)))=0 \tag{E}\end{equation*}$$ for 0 ⩽ p(t) ⩽ p 1 <1 and −1 < p 2 ⩽ p(t) ⩽ 0. The results in this paper generalize the results of [LI, T.—ZHANG, C.—XING, G.: Oscillation of third-order neutral delay differential equations, Abstr. Appl. Anal. 2012 (2012), Article ID 569201] and various results in the literature. We establish new conditions which guarantees that every solutions of (E) either oscillatory or converges to zero. Examples are considered to illustrate the main results.

On the Asymptotic Properties of Nonlinear Third-Order Neutral Delay Differential Equations with Distributed Deviating Arguments

This paper is concerned with the asymptotic properties of solutions to a third-order nonlinear neutral delay differential equation with distributed deviating arguments. Several new theorems are obtained which ensure that every solution to this equation either is oscillatory or tends to zero. Two illustrative examples are included.

Oscillation Properties of Third Order Neutral Delay Differential Equations

Oscillation criteria are established for third-order neutral delay differential equations with deviating arguments. These criteria extend and generalize those results in the literature. Moreover, some illustrating examples are also provided to show the importance of our results.

Asymptotic behavior of a third-order nonlinear neutral delay differential equation

The objective of this paper is to study asymptotic nature of a class of third-order neutral delay differential equations. By using a generalized Riccati substitution and the integral averaging technique, a new Philos-type criterion is obtained which ensures that every solution of the studied equation is either oscillatory or converges to zero. An illustrative example is included. MSC:34K11.

An oscillation criteria for third order neutral delay differential equations

In this paper, we will establish some oscillation criteria for the third-order neutral delay differential equations

The sufficient and necessary conditions of unconditional stability and the delay bound of the third-order neutral delay differential equation

In this paper, the sufficient and necessary conditions of the unconditional stability, and the delay bound of the third-order neutral delay differential equation with real constant coefficients are given. The conditions are brief and practical algebraic criterions. Furthermore, we get the delay bound.