Third-order Delay Differential Equations Research Articles

Asymptotic behaviour and boundedness of solutions for third-order stochastic differential equation with multi-delay

In the present paper, we study stochastic stability and stochastic boundedness for the stochastic differential equation (SDE) with multi-delay of third order. The derived results extend and improve some earlier results in the relevant literature, which are related to the qualitative properties of solutions to third-order delay differential equations (DDEs) and SDEs with multi-delay. Two examples are given to illustrate the results.

Iterative Criteria for Oscillation of Third-Order Delay Differential Equations with p-Laplacian Operator

ABSTRACT The aim of the paper is to study the oscillation behavior for third-order differential equations with several delays and with p-Laplacian operator. Our technique bases essentially on the presentation of sharper estimates of positive solutions of the equation studied using an iterative method. What is more, the iterative nature of the new criteria allows us to check for oscillation of all solutions, even if the known findings relevant to this fail to apply.

Third-Order Neutral Differential Equation with a Middle Term and Several Delays: Asymptotic Behavior of Solutions

This study aims to investigate the asymptotic behavior of a class of third-order delay differential equations. Here, we consider an equation with a middle term and several delays. We obtain an iterative relationship between the positive solution of the studied equation and the corresponding function. Using this new relationship, we derive new criteria that ensure that all non-oscillatory solutions converge to zero. The new findings are an extension and expansion of relevant findings in the literature. We apply our results to a special case of the equation under study to clarify the importance of the new criteria.

Numerical solution of delay differential equation using two-derivative Runge-Kutta type method with Newton interpolation

Numerical approach of two-derivative Runge-Kutta type method with three-stage fifth-order (TDRKT3(5)) is developed and proposed for solving a special type of third-order delay differential equations (DDEs) with constant delay. An algorithm based on Newton interpolation and hybrid with the TDRKT method is built to approximate the solution of third-order DDEs. In this paper, three-stage fifth-order called TDRKT3(5) method with single third derivative and multiple evaluations of the fourth derivative is highlighted to solve third-order pantograph type delay differential equations directly with the aid of the Newton interpolation method. Stability analysis of TDRKT3(5) method is investigated. The numerical experiments illustrate high efficiency and validity of the new method for solving a special class of third-order DDEs and some future works are recommended by extending proposed method to solve fractional and singularly perturbed delay differential equations.

On Sharp Oscillation Criteria for General Third-Order Delay Differential Equations

In this paper, effective oscillation criteria for third-order delay differential equations of the form, r2r1y′′′(t)+q(t)y(τ(t))=0 ensuring that any nonoscillatory solution tends to zero asymptotically, are established. The results become sharp when applied to a Euler-type delay differential equation and, to the best of our knowledge, improve all existing results from the literature. Examples are provided to illustrate the importance of the main results.

SHARP ASYMPTOTIC RESULTS FOR THIRD-ORDER LINEAR DELAY DIFFERENTIAL EQUATIONS

<abstract> In the paper, the authors propose an effective Kneser-type oscillation test for Property A for linear third-order delay differential equations that ensures that any nonoscillatory solution converges to zero asymptotically. The result is sharp when applied to Euler-type delay differential equation and improves all existing results reported in the literature. </abstract>

一类三阶半线性时滞微分方程的振动性

一类三阶半线性时滞微分方程的振动性

On oscillation of third-order noncanonical delay differential equations

In the paper, we give new criteria for the oscillation of third-order delay differential equations with noncanonical operators. Our results essentially improve and simplify the ones in Dzurina et al. (2018). The results are illustrated by a Euler-type delay differential equation.

Oscillatory and asymptotic properties of third-order quasilinear delay differential equations

In this paper, we consider a class of quasilinear third-order differential equations with a delayed argument. We establish new sufficient conditions for all solutions of such equations to be oscillatory or almost oscillatory. Those criteria improve, simplify and complement a number of existing results. The strength of the criteria obtained is tested on Euler type equations.

On asymptotic properties of solutions to third-order delay differential equations

On asymptotic properties of solutions to third-order delay differential equations

Stabilization of third-order differential equation by delay distributed feedback control

There are almost no results in mathematical literature on the exponential stability of third-order delay differential equations. One of the main purposes of the paper is to fill this gap. We propose an approach to the study of stability for third-order delay differential equations.On the basis of these results, new possibilities of stabilization by delay feedback input control are proposed.

Oscillation of third-order differential equations with noncanonical operators

New oscillation criteria for third-order delay differential equations with noncanonical operators are presented. Contrary to existing results, oscillation of the studied equation is attained via only two conditions. Our criteria not only improve, extend and significantly simplify existing ones, but the newly proposed approach could hopefully serve as a reference in the less-developed theory of noncanonical equations of higher-order. The importance of the results obtained is illustrated via Euler-type equations.

Oscillation criteria for third-order delay differential equations

The objective in this paper is to study the oscillatory and asymptotic behavior of the solutions of a linear third-order delay differential equation of the form \t\t\t(r2(t)(r1(t)y′(t))′)′+q(t)y(τ(t))=0.\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$ \\bigl( r_{2}(t) \\bigl( r_{1}(t)y'(t) \\bigr) ' \\bigr) '+q(t)y \\bigl(\\tau(t) \\bigr)= 0. $$\\end{document} We establish new oscillation criteria that can be used to test for oscillations, even when the previously known criteria fail to apply. Examples illustrating the results are also given.

On the Asymptotic Stability of Solutions for a Certain Non-autonomous Third-order Delay Differential Equation

On the Asymptotic Stability of Solutions for a Certain Non-autonomous Third-order Delay Differential Equation

Stability and boundedness of solutions of a certain n-dimensional nonlinear delay differential system of third-order

AbstractIn this paper, by defining Lyapunov functionals, we investigate proper sufficient conditions for the uniform stability of the zero solution, and also for the uniform boundedness and uniform ultimate boundedness of all solutions of a certain third-order nonlinear vector delay differential equation of the type

Stability, Boundedness, and Existence of Periodic Solutions to Certain Third-Order Delay Differential Equations with Multiple Deviating Arguments

The behaviour of solutions for certain third-order nonlinear differential equations with multiple deviating arguments is considered. By employing Lyapunov’s second method, a complete Lyapunov functional is constructed and used to establish sufficient conditions that guarantee existence of unique solutions that are periodic, uniformly asymptotically stable, and uniformly ultimately bounded. Obtained results not only are new but also include many outstanding results in the literature. Finally, the correctness and effectiveness of the results are justified with examples.

OSCILLATION THEOREMS FOR THIRD-ORDER HALF-LINEAR DELAY DIFFERENTIAL EQUATIONS

This paper conserns the oscillatory properties of the third-order halflinear delay differential equations of the form(r_2(t)[(r_1(t)x′(t))′]~α)′ + q(t)x~β{g(t)) = 0.(E)Applying suitable comparison theorems we present new criteria for oscillation of the equation(E).Results obtained generalize,improve and complement some known results in the literature,recently.

Stability and boundedness of solutions of a kind of third-order delay differential equations

This paper studies the stability and boundedness of solutions of certain nonlinear third-order delay differential equations. Sufficient conditions for the stability and boundedness of solutions for the equations considered are obtained by constructing a Lyapunov functional. Mathematical subject classification: 34K20.

Uniform Ultimate Boundedness of Solutions of Third-Order Nonlinear Delay Differential Equations

In this paper, we study the uniform boundedness and uniform ultimate boundedness of solutions of the third-order delay differential equation (*) ::: x +φ(x, ˙ x)¨ x + g( ˙ x(t r(t))) + f (x(t r(t))) = p(t, x, ˙ x, ¨), where 0 r(t) γ, γ is a positive constant, φ(x, ˙ x), g( ˙ x), f (x) and p(t, x, ˙ x, ¨) are contin- uous functions. We obtain some sufficient conditions which ensure that all the solutions of Eq.(*) are uniformly bounded and uniformly ultimately bounded. Our result revise and improve some earlier results. Mathematics Subject Classication 2000: 34K20.

On the boundedness of solutions of third-order delay differential equations

We establish certain sufficient conditions guaranteeing the boundedness of all solutions of some third-order delay differential equations.