Order Neutral Delay Differential Equations Research Articles

Oscillation criteria of fourth-order nonlinear semi-noncanonical neutral differential equations via a canonical transform

In this work first we transform the semi-noncanonical fourth order neutral delay differential equations into canonical type. This simplifies the investigations of finding the relationships between the solution and its companion function which plays an important role in the oscillation theory of neutral differential equations. Moreover, we improve these relationships based on the monotonic properties of positive solutions. We present new conditions for the oscillation of all solutions of the corresponding equation which improve the oscillation results already reported in the literature. Examples are provided to illustrate the importance of our main results. For moreinformation see https://ejde.math.txstate.edu/Volumes/2023/70/abstr.html

Amended Criteria for Testing the Asymptotic and Oscillatory Behavior of Solutions of Higher-Order Functional Differential Equations

Our interest in this article is to develop oscillation conditions for solutions of higher order differential equations and to extend recent results in the literature to differential equations of several delays. We obtain new asymptotic properties of a class from the positive solutions of an even higher order neutral delay differential equation. Then we use these properties to create more effective criteria for studying oscillation. Finally, we present some special cases of the studied equation and apply the new results to them.

Oscillation criteria of second order differential equations with positive and negative coefficients

In this paper we obtain oscillation criteria for solutions of homogeneous and nonhomogeneous cases of second order neutral differential equations with positive and negative coefficients. Our results improve and extend the results of [Oscillation criteria for a class of second order neutral delay differential equations, Appl. Math. Comput. \textbf{210}, 303--312, 2009].

Quadrature method with exponential fitting for delay differential equations having Layer behavior

In this paper, we suggest a computational method for solving delay differential equations, with one end layer, dual layer and interior layer behavior using Gaussian quadrature. The problem is initially replaced with the analogous first order neutral type delay differential equation by taking the perturbation parameter within the differentiated term. For the numerical solution with boundary layer at one endpoint, dual boundary layers and internal boundary layers, the Gaussian two-point quadrature scheme was extracted with exponential fitting. Using model examples, the suggested approach is used for various perturbation and delay parameter values. The numerical scheme is validated and supported by the comparison of maximum errors with the other results in the literature. Convergence of the method is examined. For various delay parameter values, the layer structure is depicted in graphs.

Oscillation of First Order Neutral Differential Equations with Delay

A class of first order neutral delay differential equations are investigated, and sufficient condition is derived for all solutions to be oscillatory. This result solves an open problem in the literature.

Hybrid Multistep Block Method for Solving Neutral Delay Differential Equations

The initial-value problem for first order single linear neutral delay differential equations (NDDEs) of constant and pantograph delay types have been solved by using hybrid multistep block method. The method has been derived by applying Taylor series interpolation polynomial and implementing the predictor-corrector formulas in PE(CE)m mode where m is the number of iterations for the proposed method. Both types of NDDEs will be solved at two-point simultaneously including the off-step point with constant step-size. In order to find the solution for NDDEs, the delay solutions of the unknown function will be interpolated using Lagrange interpolation polynomial and the derivative of the delay solutions will be obtained by applying divided difference formula. The order, consistency and convergence of the proposed method have been discussed in detail in the methods section. The properties of stability region for NDDEs have also been analysed. Numerical results presented have concluded that the proposed method is comparable with the existing method and is assumed to be reliable for solving first order NDDEs with constant and pantograph delay.

Oscillation of one kind of second order neutral delay differential equations

This paper is dedicated to discussing the oscillation of the second order neutral delay differential equations (r(t)(z´(t))α)´ + q(t)f(xβ(σ(t))) = 0, where z(t) = x(t) + p(t)x(τ(t)). Sufficient conditions are provided by Riccati transformation comparing with related first order differential inequalities and differential equations. Results obtained in this paper have extended and improved conclusions contained in other literatures. Several illustrative examples are presented.

Oscillation of one kind of second order neutral delay differential equations

This paper is dedicated to discussing the oscillation of the second order neutral delay differential equations (r(t)(z´(t))α)´ + q(t)f(xβ(σ(t))) = 0, where z(t) = x(t) + p(t)x(τ(t)). Sufficient conditions are provided by Riccati transformation comparing with related first order differential inequalities and differential equations. Results obtained in this paper have extended and improved conclusions contained in other literatures. Several illustrative examples are presented.

Oscillation criteria for second-order quasi-linear neutral functional differential equation

In this work, new sufficient conditions for oscillation of solution of second order neutral delay differential equation are established. One objective of our paper is to further simplify and complement some results which were published lately in the literature. In order to support our results, we introduce illustrating examples.

An oscillation criterion in 4{th}-order neutral differential equations with a continuously distributed delay

In this paper, a class of 4{th}-order neutral delay differential equations with continuously distributed delay is studied. We establish a new oscillation criterion using the Riccati transformation. An example illustrating the results is also given.

Stability, boundedness, and square integrability of solutions to third order neutral differential equations with delay

In this paper, the asymptotic behavior of solutions of a class of non-autonomous third order neutral delay differential equations is studied. Results on the stability, boundedness, and the square integrability of solutions and their derivatives are obtained. An example to illustrate the results is included.

Oscillation criteria for a class of third order neutral distributed delay differential equations with damping

Oscillation criteria for a class of third order neutral distributed delay differential equations with damping

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.

Oscillation by Impulses for a Second Order Neutral Delay Differential Equations

Oscillation by Impulses for a Second Order Neutral Delay Differential Equations

Asymptotic behaviour of nonoscillating solutions of neutral delay differential equations of the second order with impulses

In this paper, we consider a certain class of second order neutral delay differential equations with constant impulsive jumps and obtain some sufficient conditions for the asymptotic decay of all of its non-oscillating solutions. An example is provided to illustrate the main result.

Asymptotic behaviour of nonoscillating solutions of neutral delay differential equations of the second order with impulses

In this paper, we consider a certain class of second order neutral delay differential equations with constant impulsive jumps and obtain some sufficient conditions for the asymptotic decay of all of its non-oscillating solutions. An example is provided to illustrate the main result.

English

English

On oscillatory nonlinear second order neutral delay differential equations

On oscillatory nonlinear second order neutral delay differential equations

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.

Computational method for singularly perturbed delay differential equations with twin layers or oscillatory behaviour

In this paper, we have presented a computational method for solving singularly perturbed delay differential equations with twin layers or oscillatory behaviour. In this method, the original second order singularly perturbed delay differential equation is replaced by an asymptotically equivalent first order neutral type delay differential equation. Then, we have employed numerical integration and linear interpolation to get tridiagonal system. This tridiagonal system is solved efficiently by using discrete invariant imbedding algorithm. Several model examples are solved, and computational results are presented by taking various values of the delay parameter and perturbation parameter. We have also discussed the convergence of the method.