Second-order Neutral Differential Equations Research Articles

Second-Order Neutral Differential Equations with a Sublinear Neutral Term: Examining the Oscillatory Behavior

This article highlights the oscillatory properties of second-order Emden–Fowler delay differential equations featuring sublinear neutral terms and multiple delays, encompassing both canonical and noncanonical cases. Through the proofs of several theorems, we investigate criteria for the oscillation of all solutions to the equations under study. By employing the Riccati technique in various ways, we derive results that expand the scope of previous research and enhance the cognitive understanding of this mathematical domain. Additionally, we provide three illustrative examples to demonstrate the validity and applicability of our findings.

Approximate controllability of damped second-order neutral differential equations with state-dependent delay

ABSTRACT This article discusses the approximate controllability of damped second-order neutral differential equations with state-dependent delay. The results are obtained using strongly continuous cosine family theories and fixed-point theories. Assuming approximate controllability of the corresponding equation, we obtain sufficient conditions for approximate controllability of the nonlinear second-order equations. An application are provided to demonstrate how the proposed result can be applied.

Superlinear distributed deviating arguments to study second-order neutral differential equations

Superlinear distributed deviating arguments to study second-order neutral differential equations

Oscillation criteria for mixed neutral differential equations

<abstract><p>In this study, we aim to contribute to the increasing interest in functional differential equations by obtaining new theorems for the oscillation of second-order neutral differential equations of mixed type in a non-canonical form. The results obtained here improve and extend those reported in the literature. The applicability of the results is illustrated by several examples.</p></abstract>

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.

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

Second-Order Neutral Differential Equations with Distributed Deviating Arguments: Oscillatory Behavior

In this paper, new criteria for a class oscillation of second-order delay differential equations with distributed deviating arguments were established. Our method mainly depends on making sharper estimates for the non-oscillatory solutions of the studied equation. By using the Ricati technique and comparison theorems that compare the studied equations with first-order delay differential equations, we obtained new and less restrictive conditions that ensure the oscillation of all solutions of the studied equation. Further, we give an illustrative example.

Necessary and Sufficient Conditions for Oscillations to a Second-Order Neutral Differential Equations with Impulses

Necessary and Sufficient Conditions for Oscillations to a Second-Order Neutral Differential Equations with Impulses

PERIODIC SOLUTIONS OF A CLASS OF SECOND ORDER NEUTRAL DIFFERENTIAL EQUATIONS WITH MULTIPLE DIFFERENT DELAYS

The present work mainly probes into the existence and uniqueness of periodic solutions for a class of second-order neutral differential equations with multiple delays. Our approach is based on using Banach and Krasnoselskii's fixed point theorems as well as the Green's function method. Besides, two examples are exhibited to validate the effectiveness of our findings which complement and extend some relevant ones in the literature.

Second-order impulsive differential systems of mixed type: oscillation theorems

In this paper, we obtain necessary and sufficient conditions for the oscillation of solutions to a second-order neutral differential equation with impulses. Two examples are provided to show the effectiveness and feasibility of the main results. Our main tool is Lebesgue’s dominated convergence theorem.

Some conditions for the oscillation of second-order differential equations with several mixed delays

In this work, we obtain necessary and sufficient conditions for the oscillation of the solutions to a second-order neutral differential equation with mixed delays. Two examples are provided to show effectiveness and feasibility of main results. Our main tool is the Lebesgue’s Dominated Convergence theorem.

Oscillatory Behavior of Second-Order Neutral Differential Equations

In this paper, we study oscillatory properties of neutral differential equations. Moreover, we discuss some examples that show the effectiveness and the feasibility of the main results.

An Oscillation Test for Solutions of Second-Order Neutral Differential Equations of Mixed Type

It is easy to notice the great recent development in the oscillation theory of neutral differential equations. The primary aim of this work is to extend this development to neutral differential equations of mixed type (including both delay and advanced terms). In this work, we consider the second-order non-canonical neutral differential equations of mixed type and establish a new single-condition criterion for the oscillation of all solutions. By using a different approach and many techniques, we obtain improved oscillation criteria that are easy to apply on different models of equations.

Existence of nonoscillatory solutions of second-order neutral differential equations

In this study we shall obtain some sufficient conditions for the existence of positive solutions of variable coefficient nonlinear second-order neutral differential equation with distributed deviating arguments. For some different cases of the range of p(t) by using Banach contraction principle we will give some sufficient conditions for the nonoscillatory solutions of second-order neutral differential equation. With this purpose we will use fixpoint theorem. At the end of the research, there is an example that meets the conditions we have given. Our results improve and extend some existing results.

Oscillation of a kind of second-order nonlinear neutral difference equations

This article deals with the necessary and sufficient conditions for the oscillation of a class of nonlinear second-order neutral difference equations for four distinct ranges of the neutral coefficient p(n). Our study allow that the nonlinear function is either strongly sublinear or strongly superlinear. Some examples are given to illustrate our main results.

Oscillation Results for Second-Order Neutral Functional Differential Equations

In this article, we obtain several comparison theorems for the second-order neutral differential equation , t ⩾ t 0, where γ, λ, β are ratios of positive odd integers. We compare above equation with the first-order differential inequalities in the sense that the absence of the eventually positive solutions of these first-order inequalities implies the oscillation of the studied equation.

On oscillation of second-order noncanonical neutral differential equations

In the present work, we study the second-order neutral differential equation and formulate new oscillation criteria for this equation. Our conditions differ from the earlier ones. Also, our results are expansions and generalizations of some previous results. Examples to illustrate the main results are included.

New oscillation criteria for second-order neutral differential equations with distributed deviating arguments

In this work, we create new oscillation conditions for solutions of second-order differential equations with continuous delay. The new criteria were created based on Riccati transformation technique and comparison principles. Furthermore, we obtain iterative criteria that can be applied even when the other criteria fail. The results obtained in this paper improve and extend the relevant previous results as illustrated by examples.

Second-order Emden–Fowler neutral differential equations: A new precise criterion for oscillation

This study aims at offering a new criterion for the oscillation of the solutions of Emden–Fowler second-order neutral differential equations. The approach used presents a non-traditional Riccati substitution and takes into account all the delay functions, which had been neglected in previous analyses. The new results essentially improve and simplify some well-known results reported in the literature. Furthermore, the new criterion provides precise results in the ordinary case (e.g. Euler-type equations), whereas the existing results fail in this case.

Second-Order Neutral Differential Equations: Improved Criteria for Testing the Oscillation

The main purpose of this study is to establish new improved conditions for testing the oscillation of solutions of second-order neutral differential equation r l u ′ l γ ′ + q l x β σ l = 0 , where l ≥ l 0 and u l ≔ x l + p x ϱ l . By optimizing the commonly used relationship x > 1 − p u , we obtain new criteria that give sharper results for oscillation than the previous related results. Moreover, we obtain criteria of an iterative nature. Our new results are illustrated by an example.