Solutions Of Neutral Differential Equations Research Articles

On the monotonic properties and oscillatory behavior of solutions of neutral differential equations

Abstract In this work, we study new asymptotic properties of positive solutions of the even-order neutral differential equation with the noncanonical operator. The new properties are iterative, which means they can be used several times. We also use these properties to obtain new criteria for oscillation of the studied equation.

On the existence and uniqueness of positive periodic solutions of neutral differential equations

On the existence and uniqueness of positive periodic solutions of neutral differential equations

A Study of the Monotonic Properties of Solutions of Neutral Differential Equations and Their Applications

In this paper, we aim to study the monotonic properties of the solutions of a class of neutral delay differential equations. The importance of this study lies in the fact that the monotonic properties largely control the study of the oscillation and asymptotic behaviour of the solutions to delay differential equations. Then, by using the new properties, we create improved criteria for testing the oscillation of solutions to the studied equation. We also find new criteria that can be applied more than once. Moreover, we discuss the importance and novelty of the results through the application to a special case of the studied equation.

New Conditions for Testing the Asymptotic and Oscillatory Behavior of Solutions of Neutral Differential Equations of the Fourth Order

In this work, in the noncanonical case, we find new properties for a class of positive solutions of fourth-order differential equations. These properties allow us to obtain iterative criteria that exclude positive decreasing solutions, and we then establish sufficient conditions to guarantee that all solutions to the examined equation oscillate. The importance of applying the results to a special case of the investigated equation is demonstrated.

Existence and Monotone Iterative Approximation of Solutions for Neutral Differential Equations with Generalized Fractional Derivatives

We study the existence and monotone iterative approximation of mild solutions of fractional-order neutral differential equations involving a generalized fractional derivative of order 0 < α < 1 which can be reduced to Riemann–Liouville or Hadamard fractional derivatives. The existence of mild solutions is obtained via fixed point techniques in a partially ordered space. The approach is constructive and can be applied numerically. In particular, we construct a monotone sequence of functions converging to a solution which is illustrated by a numerical example.

Globally Exponential Stability of Piecewise Pseudo Almost Periodic Solutions for Neutral Differential Equations with Impulses and Delays

Globally Exponential Stability of Piecewise Pseudo Almost Periodic Solutions for Neutral Differential Equations with Impulses and Delays

Qualitative Behavior of Unbounded Solutions of Neutral Differential Equations of Third-Order

New oscillatory properties for the oscillation of unbounded solutions to a class of third-order neutral differential equations with several deviating arguments are established. Several oscillation results are established by using generalized Riccati transformation and a integral average technique under the case of unbounded neutral coefficients. Examples are given to prove the significance of new theorems.

Oscillation Criteria for Solutions of Neutral Differential Equations of Impulses Effect with Positive and Negative Coefficients

In this paper, some necessary and sufficient conditions are obtained to ensure the oscillatory of all solutions of the first order impulsive neutral differential equations. Also, some results in the references have been improved and generalized. New lemmas are established to demonstrate the oscillation property. Special impulsive conditions associated with neutral differential equation are submitted. Some examples are given to illustrate the obtained results.

An Approach for Studying Asymptotic Properties of Solutions of Neutral Differential Equations

The paper is devoted to the study of oscillation of even-order neutral differential equations. New Kamenev-type oscillation criteria are established, and they essentially improve and complement some the well-known results reported in the literature. Ideas of symmetry help us determine the correct ways to study these topics and show us the correct direction, because they are often invisible. To illustrate the main results, some examples are mentioned.

New Aspects for Non-Existence of Kneser Solutions of Neutral Differential Equations with Odd-Order

Some new oscillatory and asymptotic properties of solutions of neutral differential equations with odd-order are established. Through the new results, we give sufficient conditions for the oscillation of all solutions of the studied equations, and this is an improvement of the relevant results. The efficiency of the obtained criteria is illustrated via example.

An Asymptotic Result for neutral differential equations

Abstract We obtain asymptotic result for the solutions of neutral differential equations. Our technique depends on characteristic equations.

Legendre wavelet solution of neutral differential equations with proportional delays

The aim of this paper is to solve neutral differential equations with proportional delays by using Legendre wavelet method. Using orthonormal polynomials is the main advantage of this method since it enables a decrease in the computational cost and runtime. Some examples are displayed to illustrate the efficiency and accuracy of the proposed method. Numerical results are compared with various numerical methods in literature and show that the present method is very effectual in solving neutral differential equations with proportional delays.

On abstract neutral differential equations with state-dependent delay

In this paper, we study the existence and uniqueness of mild and strict solutions for abstract neutral differential equations with state-dependent delay. In the last section, some examples are presented.

Existence and Uniqueness of Solutions for Abstract Neutral Differential Equations with State-Dependent Delay

We study the existence and uniqueness of mild and strict solutions for abstract neutral differential equations with state-dependent delay. Some examples related to partial neutral differential equations are presented.

Об устойчивости решений дифференциальных уравнений нейтрального типа с распределенным запаздыванием

Об устойчивости решений дифференциальных уравнений нейтрального типа с распределенным запаздыванием

On the Nature of Solutions of Neutral Differential Equations with Periodic Coefficients

On the Nature of Solutions of Neutral Differential Equations with Periodic Coefficients

On implicit abstract neutral nonlinear differential equations

In this paper we continue our developments in Hernandez and O'Regan (J Funct Anal 261:3457---3481, 2011) on the existence of solutions for abstract neutral differential equations. In particular we extend the results in Hernandez and O'Regan (J Funct Anal 261:3457---3481, 2011) for the case of implicit nonlinear neutral equations and we focus on applications to partial "nonlinear" neutral differential equations. Some applications involving partial neutral differential equations are presented.

Representation of solutions of neutral differential equations with delay and linear parts defined by pairwise permutable matrices

Representation of solutions of neutral differential equations with delay and linear parts defined by pairwise permutable matrices

On [formula omitted]-Hölder classical solutions for non-autonomous neutral differential equations: The nonlinear case

In this paper we continue our developments in [19] on the existence of classical solutions for abstract neutral differential equations. In the current work we extend the results in [19] for nonlinear neutral differential equations. Some applications involving nonlinear partial neutral differential equations are presented.

Asymptotic Behavior of Solutions of Neutral Difference Equations Dealing with Mechanical Vibration Problems

Asymptotic behavior is studied for solutions of neutral difference equations dealing with mechanical vibration problems and other related topics, and some theorems have been obtained.