Second-order Neutral Delay Research Articles

A high order method for oscillatory delay differential equations

This paper addresses the oscillatory properties of a class of second-order neutral delay differential equations (NDDEs) and introduces a numerical scheme based on a fourth-order predictor-corrector multistep method for solving NDDEs of this type. An example in the family of oscillatory equations has been integrated by using the proposed numerical scheme. Results confirm the theoretical assumptions.

Sharp results for oscillation of second-order neutral delay differential equations

The aim of the present paper is to continue earlier works by the authors on the oscillation problem of second-order half-linear neutral delay differential equations. By revising the set method, we present new oscillation criteria which essentially improve a number of related ones from the literature. A couple of examples illustrate the value of the results obtained.

New oscillation criteria and some refinements for second-order neutral delay dynamic equations on time scales

In this paper, we present more effective criteria for oscillation of second-order half-linear neutral dynamic equations with delayed arguments. Our results essentially improve, complement, and simplify several related ones in the literature. Some examples are given to illustrate our main results.

New oscillation criteria for second-order neutral delay dynamic equations with a non-positive neutral term on time scales

In this paper, we investigate the oscillatory behavior of solutions of a class of secondorder nonlinear neutral delay dynamic equations with non-positive coefficient where α ≥ β are ratios of odd positive integers and z(t) := x(t) - p(t)x(τ (t)). The obtained results guarantee that all solutions are oscillatory. Illustrative examples are provided.

New Sufficient Conditions for Oscillation of Second-Order Neutral Delay Differential Equations

In this work, new sufficient conditions for the oscillation of all solutions of the second-order neutral delay differential equations with the non-canonical operator are established. Using a generalized Riccati substitution, we obtained criteria that complement and extend some previous results in the literature.

New Criteria for Sharp Oscillation of Second-Order Neutral Delay Differential Equations

In this paper, new oscillation criteria for second-order half-linear neutral delay differential equations are established, using a recently developed method of iteratively improved monotonicity properties of a nonoscillatory solution. Our approach allows removing several disadvantages which were commonly associated with the method based on a priori bound for the nonoscillatory solution, and deriving new results which are optimal in a nonneutral case. It is shown that the newly obtained results significantly improve a large number of existing ones.

On the Oscillation of second order nonlinear neutral delay differential equations

AbstractA class of second-order neutral delay differential equations is considered. New oscillation criteria are established to complement and improve some known results in the literature. Two examples are given to support our results.

Second-order impulsive differential systems with mixed and several delays

In this work, we present new necessary and sufficient conditions for the oscillation of a class of second-order neutral delay impulsive differential equations. Our oscillation results complement, simplify and improve recent results on oscillation theory of this type of nonlinear neutral impulsive differential equations that appear in the literature. An example is provided to illustrate the value of the main results.

New Oscillation Theorems for Second-Order Differential Equations with Canonical and Non-Canonical Operator via Riccati Transformation

In this work, we prove some new oscillation theorems for second-order neutral delay differential equations of the form (a(ξ)((v(ξ)+b(ξ)v(ϑ(ξ)))′))′+c(ξ)G1(v(κ(ξ)))+d(ξ)G2(v(ς(ξ)))=0 under canonical and non-canonical operators, that is, ∫ξ0∞dξa(ξ)=∞ and ∫ξ0∞dξa(ξ)<∞. We use the Riccati transformation to prove our main results. Furthermore, some examples are provided to show the effectiveness and feasibility of the main results.

On the qualitative behavior of the solutions to second-order neutral delay differential equations

Differential equations of second order appear in numerous applications such as fluid dynamics, electromagnetism, quantum mechanics, neural networks and the field of time symmetric electrodynamics. The aim of this work is to establish necessary and sufficient conditions for the oscillation of the solutions to a second-order neutral differential equation. First, we have taken a single delay and later the results are generalized for multiple delays. Some examples are given and open problems are presented.

On the Asymptotic Behavior of a Class of Second-Order Non-Linear Neutral Differential Equations with Multiple Delays

In this work, we present some new sufficient conditions for the oscillation of a class of second-order neutral delay differential equation. Our oscillation results, complement, simplify and improve recent results on oscillation theory of this type of non-linear neutral differential equations that appear in the literature. An example is provided to illustrate the value of the main results.

New Oscillation Criteria for Second-Order Neutral Delay Dynamic Equations with a Nonpositive Neutral Term on Time Scales

New Oscillation Criteria for Second-Order Neutral Delay Dynamic Equations with a Nonpositive Neutral Term on Time Scales

Oscillation and Asymptotic Behavior of Second-Order Neutral Delay Difference Equations with Variable Delays

Oscillation and Asymptotic Behavior of Second-Order Neutral Delay Difference Equations with Variable Delays

Existence conditions for periodic solutions of second-order neutral delay differential equations with piecewise constant arguments

Abstract In this paper, we describe a method to solve the problem of finding periodic solutions for second-order neutral delay-differential equations with piecewise constant arguments of the form x″(t) + px″(t − 1) = qx([t]) + f(t), where [⋅] denotes the greatest integer function, p and q are nonzero real or complex constants, and f(t) is complex valued periodic function. The method reduces the problem to a system of algebraic equations. We give explicit formula for the solutions of the equation. We also give counter examples to some previous findings concerning uniqueness of solution.

An improved approach for studying oscillation of second-order neutral delay differential equations

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

Dynamic analysis of a class of neutral delay model based on the Runge-Kutta algorithm

In this paper, we study the dynamics of a class of second-order neutral delay nonlinear models. This study is applicable to many fields, such as engineering, cybernetics, and physics. We use the Runge-Kutta algorithm and the Riccati transform method. First, we give a neutral delay nonlinear model based on the Runge-Kutta algorithm. Then, we study the dynamic characteristics of the neutral delay model and establish some new sufficient conditions for the oscillation. The results of our research are new, and these results promote and improve the results already available. The results are also verified by numerical experiments. The neutral delay nonlinear model has an important application in engineering, cybernetics, and physics. Therefore, the study of this paper has great help and promotion to engineering, cybernetics, and physics.

On the method of finding periodic solutions of second-order neutral differential equations with piecewise constant arguments

This paper provides a method of finding periodical solutions of the second-order neutral delay differential equations with piecewise constant arguments of the form x''(t)+px''(t-1)=qx(2[frac{t+1}{2}])+f(t), where [cdot] denotes the greatest integer function, p and q are nonzero constants, and f is a periodic function of t. This reduces the 2n-periodic solvable problem to a system of n+1 linear equations. Furthermore, by applying the well-known properties of a linear system in the algebra, all existence conditions are described for 2n-periodical solutions that render explicit formula for these solutions.

Oscillation of nonlinear second-order neutral delay differential equations

Oscillation of nonlinear second-order neutral delay differential equations

New oscillation criteria for second-order neutral delay dynamic equations

New oscillation criteria for second-order neutral delay dynamic equations

Oscillation criteria for second-order neutral delay differential equations

Oscillation criteria for second-order neutral delay differential equations