Neutral Differential Equations Research Articles

Oscillatory behavior of second-order nonlinear noncanonical neutral differential equations

Abstract This paper discusses the oscillatory behavior of solutions to a class of second-order nonlinear noncanonical neutral differential equations. Sufficient conditions for all solutions to be oscillatory are given. Examples are provided to illustrate all the main results obtained.

On the Monotonic and Asymptotic Properties of Positive Solutions to Third-Order Neutral Differential Equations and Their Effect on Oscillation Criteria

The monotonic properties of positive solutions to functional differential equations of the third order are examined in this paper. It is generally known that by optimizing the relationships between a solution and its corresponding function, as well as its derivatives, one can improve the oscillation criterion for neutral differential equations. Based on this, we obtain new relationships and inequalities and test their effect on the oscillation parameters of the studied equation. To obtain the oscillation parameters, we used Riccati techniques and comparison with lower-order equations. Finally, the progress achieved in oscillation theory for third-order equations was measured by comparing our results with previous relevant results.

Positive periodic solutions of third-order neutral differential equations with delayed derivative terms

By applying fixed point index theory on cones, the existence results of positive 2π-periodic solutions are obtained for the third-order neutral differential equation with delayed derivative terms in nonlinearity(x(t)−cx(t−δ))‴+a(t)x(t)=f(t,x(t),x(t−τ0),x′(t−τ1),x″(t−τ2)),t∈R under the condition that the nonlinear term f satisfies superlinear or sublinear growth, where constants δ>0,|c|<1, a:R→(0,+∞) and f:R×[0,+∞)2×R2→[0,+∞) are continuous functions which are 2π periodic in t and constants τ0,τ1,τ2>0.

Oscillatory Properties Test for Even-Order Di§erential Equations of Neutral type

This paper presents a study on the oscillatory behavior of solutions to even-order neutral differential equations involving p-Laplacian-like operator. We obtain oscillation criteria using techniques from first-order delay differential equations, Riccati technique and integral averages technique. The results of this work contribute to a deeper understanding of even-order differential equations and their connections to various branches of mathematics and practical sciences. The findings emphasize the importance of continued research in this area.

New oscillation and non-oscillation criteria for third order neutral differential equations with distributed deviating arguments

New oscillation and non-oscillation criteria for third order neutral differential equations with distributed deviating arguments

Nonexistence of Kneser solution of neutral delay difference equation

By creating suitable standards for the nonexistence of so-called Kneser solutions, this study seeks to augment the third order neutral delay difference equations current oscillation results. The results of combining new and previous findings. All of the answers to the studied equations oscillate thanks to our work.

More Effective Conditions for Testing the Oscillatory Behavior of Solutions to a Class of Fourth-Order Functional Differential Equations

This paper presents an investigation into the qualitative behavior of solutions for a specific class of fourth-order half-linear neutral differential equations. The main objective of this study is to improve the relationship between the solution and its corresponding function. By developing improved relationships, a novel criterion is proposed to determine the oscillatory behavior of the studied equation. The exclusion of positive solutions is achieved through a comparative approach in which the examined equation is compared to second-order equations. Additionally, the significance of the obtained results is demonstrated by applying them to various illustrative examples.

New Monotonic Properties for Solutions of a Class of Functional Differential Equations and Their Applications

This paper delves into the enhancement of asymptotic and oscillatory behaviors in solutions to even-order neutral differential equations with multiple delays. The main objective is to establish improved inequalities to advance the understanding of oscillation theory for these equations. The paper’s approach is centered on improving the understanding of the intricate relationship between solutions and their corresponding functions. This is achieved by harnessing the modified monotonic properties of positive solutions, which provide valuable insights into oscillation behavior. Furthermore, leveraging the symmetry between positive and negative solutions, we derived criteria that ensure oscillation for all solutions, with a specific emphasis on excluding only positive solutions. To illustrate the significance of our findings, we provide an illustrative example.

Fourth-Order Neutral Differential Equation: A Modified Approach to Optimizing Monotonic Properties

In this article, we investigate some qualitative properties of solutions to a class of functional differential equations with multi-delay. Using a modified approach, we first derive a number of optimized relations and inequalities that relate the solution xs to its corresponding function zs and its derivatives. After classifying the positive solutions, we follow the Riccati approach and principle of comparison, where fourth-order differential equations are compared with first-order differential equations to obtain conditions that exclude the positive solutions. Then, we introduce new oscillation conditions. With regard to previous relevant results, our results are an extension and complement to them. This work has theoretical significance in that it uncovers some new relationships that aid in developing the oscillation theory of higher-order equations in addition to the applied relevance of neutral differential equations.

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

Approximate Controllability of Neutral Differential Systems with Fractional Deformable Derivatives

This article deals with the existence and uniqueness of solutions, as well as the approximate controllability of fractional neutral differential equations (ACFNDEs) with deformable derivatives. The findings are achieved using Banach’s, Krasnoselskii’s, and Schauder’s fixed-point theorems and semigroup theory. Three numerical examples are used to illustrate the application of the theories discussed in the conclusion.

Noncanonical Emden–Fowler neutral differential equations: New criteria for oscillation

In this study, we extend the approach used to study the oscillatory behavior of delay differential equations to neutral equations. In the noncanonical case, we establish a new one‐condition criterion that guarantees the oscillation of a class of second‐order Emden‐Fowler neutral differential equations. The symmetry between the positive and negative solutions of the studied equation plays an important role in the proof of our results. Finally, we present an example to compare our results with previous relevant results.

Asymptotic Synchronization of Nonlinear Functional Neutral Delay Difference Equations with Variable Coefficients

Asymptotic Synchronization of Nonlinear Functional Neutral Delay Difference Equations with Variable Coefficients

Optimizing the Monotonic Properties of Fourth-Order Neutral Differential Equations and Their Applications

We investigate the oscillation of the fourth-order differential equation for a class of functional differential equations of the neutral type. We obtain a new single-oscillation criterion for the oscillation of all the solutions of our equation. We establish new monotonic properties for some cases of positive solutions of the studied equation. Moreover, we improve these properties by using an iterative method. This development of monotonic properties contributes to obtaining new and more efficient criteria for verifying the oscillation of the equation. The results obtained extend and improve previous findings in the literature by using an Euler-type equation as an example. The importance of the results was clarified by applying them to some special cases of the studied equation. The fourth-order delay differential equations have great practical importance due to their wide applications in civil, mechanical, and aeronautical engineering. Research on this type of equation is still ongoing due to its remarkable importance in many fields.

Sv-asymptotically T-periodic solutions for some class of neutral differential equations — Model of the heat equation

In this paper, we aim to present the concept of [Formula: see text]-asymptotically T-periodic functions taking values in a Banach space and investigate some of their properties. Also, we establish conditions under which semi linear evolution equations in a Banach space have a unique global mild [Formula: see text]-asymptotically T-periodic solution. Then, we apply the results obtained to prove the existence and uniqueness of [Formula: see text]-asymptotically [Formula: see text]-periodic mild solutions to a nonautonomous semi linear differential equations.

New Oscillation Theorems for Second-Order Superlinear Neutral Differential Equations with Variable Damping Terms

In this paper, we investigate the oscillatory behavior of solutions of second-order differential equations with a superlinear neutral term and a damping term in noncanonical forms. We do not place any additional conditions on the damping term. Therefore, our results apply to new classes of equations that were not covered by the previous criteria. According to symmetry between the negative and positive solutions of the studied equation, we present some new criteria that ensure the oscillation of all solutions by using the Riccati transformation and comparison method. We provide an example to illustrate our main results.

Oscillation Analysis Algorithm for Nonlinear Second-Order Neutral Differential Equations

Differential equations are useful mathematical tools for solving complex problems. Differential equations include ordinary and partial differential equations. Nonlinear equations can express the nonlinear relationship between dependent and independent variables. The nonlinear second-order neutral differential equations studied in this paper are a class of quadratic differentiable equations that include delay terms. According to the t-value interval in the differential equation function, a basis is needed for selecting the initial values of the differential equations. The initial value of the differential equation is calculated with the initial value calculation formula, and the existence of the solution of the nonlinear second-order neutral differential equation is determined using the condensation mapping fixed-point theorem. Thus, the oscillation analysis of nonlinear differential equations is realized. The experimental results indicate that the nonlinear neutral differential equation can analyze the oscillation behavior of the circuit in the Colpitts oscillator by constructing a solution equation for the oscillation frequency and optimizing the circuit design. It provides a more accurate control for practical applications.

Approximation of solutions to abstract neutral differential equations with non-instantaneous impulses

Approximation of solutions to abstract neutral differential equations with non-instantaneous impulses

Chaplygin’s method for second-order neutral differential equations with piecewise constant deviating arguments

Chaplygin’s method for second-order neutral differential equations with piecewise constant deviating arguments

Neutral Differential Equations of Higher-Order in Canonical Form: Oscillation Criteria

This paper aims to study a class of neutral differential equations of higher-order in canonical form. By using the comparison technique, we obtain sufficient conditions to ensure that the studied differential equations are oscillatory. The criteria that we obtained are to improve and extend some of the results in previous literature. In addition, an example is given that shows the applicability of the results we obtained.