Oscillation Theorems for Certain Even Order Delay Differential Equations Involving General Means

2006 ◽  
Vol 13 (2) ◽  
pp. 383-394
Author(s):  
Zhiting Xu ◽  
Peixuan Weng
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Even Order ◽  
Delay Differential ◽  
Oscillation Theorems

Abstract By using the general means, we establish some oscillation theorems for the even order delay differential equation (𝑟(𝑡)|𝑥(𝑛–1)(𝑡)| α–1𝑥(𝑛–1)(𝑡))′ + 𝐹(𝑡, 𝑥[𝑔(𝑡)]) = 0, where α > 0 is a constant, , and 𝑔 ∈ 𝐶([𝑡0, ∞), ℝ). The results obtained extend and improve some results known in the literature.

scholarly journals Asymptotic and Oscillatory Properties of Noncanonical Delay Differential Equations

2021 ◽  
Vol 5 (4) ◽  
pp. 259
Author(s):  
Osama Moaaz ◽  
Clemente Cesarano ◽  
Sameh Askar
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Asymptotic Properties ◽  
Oscillatory Solutions ◽  
Even Order ◽  
Delay Differential ◽  
New Criteria ◽  
Oscillatory Properties

In this work, by establishing new asymptotic properties of non-oscillatory solutions of the even-order delay differential equation, we obtain new criteria for oscillation. The new criteria provide better results when determining the values of coefficients that correspond to oscillatory solutions. To explain the significance of our results, we apply them to delay differential equation of Euler-type.

scholarly journals New Asymptotic Properties of Positive Solutions of Delay Differential Equations and Their Application

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1971
Author(s):  
Osama Moaaz ◽  
Clemente Cesarano
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Positive Solutions ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Asymptotic Properties ◽  
Even Order ◽  
Delay Differential ◽  
New Criteria ◽  
Noncanonical Operator

In this study, new asymptotic properties of positive solutions of the even-order delay differential equation with the noncanonical operator are established. The new properties are of an iterative nature, which allows it to be applied several times. Moreover, we use these properties to obtain new criteria for the oscillation of the solutions of the studied equation using the principles of comparison.

Oscillations of Neutral Delay Differential Equations

1986 ◽  
Vol 29 (4) ◽  
pp. 438-445 ◽  
Author(s):  
G. Ladas ◽  
Y. G. Sficas
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Neutral Delay Differential Equation ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

AbstractThe oscillatory behavior of the solutions of the neutral delay differential equationwhere p, τ, and a are positive constants and Q ∊ C([t0, ∞), ℝ+), are studied.

scholarly journals Solution Of Singularly Perturbed Delay Differential Equations Using Liouville Green Transformation

2021 ◽  
Vol 12 (4) ◽  
pp. 325-335
Author(s):  
M. Adilaxmi , Et. al.
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Perturbation Problem ◽  
Delay Differential ◽  
Singularly Perturbation ◽  
The Given

This paper envisages the use of Liouville Green Transformation to find the solution of singularly perturbed delay differential equations. First, using Taylor series, the given singularly perturbed delay differential equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. The method is demonstrated by implementing several model examples by taking various values for the delay parameter and perturbation parameter.

scholarly journals Oscillation of even-order neutral differential equations via comparison principles

2014 ◽  
Vol 30 (3) ◽  
pp. 293-300
Author(s):  
J. DZURINA ◽  
◽  
B. BACULIKOVA ◽  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Order Differential Equation ◽  
Higher Order ◽  
Comparison Principles ◽  
Neutral Differential Equations ◽  
First Order ◽  
Even Order ◽  
Delay Differential

In the paper we offer oscillation criteria for even-order neutral differential equations, where z(t) = x(t) + p(t)x(τ(t)). Establishing a generalization of Philos and Staikos lemma, we introduce new comparison principles for reducing the examination of the properties of the higher order differential equation onto oscillation of the first order delay differential equations. The results obtained are easily verifiable.

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

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1675
Author(s):  
Irena Jadlovská ◽  
George E. Chatzarakis ◽  
Jozef Džurina ◽  
Said R. Grace
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Nonoscillatory Solution ◽  
Third Order ◽  
Oscillation Criteria ◽  
Delay Differential

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.

scholarly journals Computation of First order Delay Differential Equations via Simpson Block Method

2020 ◽  
Vol 5 (2) ◽  
Author(s):  
Ridwanulahi I Abdulganiy ◽  
Olusheye A Akinfenwa ◽  
Osaretin E Enobabor ◽  
Blessing I Orji ◽  
Solomon A Okunuga
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Step Width ◽  
Block Method ◽  
Delay Term ◽  
First Order ◽  
Collocation Technique ◽  
Delay Differential

A family of Simpson Block Method (SBM) is proposed for the numerical integration of Delay Differential Equations (DDEs). The methods are developed through multistep collocation technique using constant step width. The convergence and accuracy of the methods are established through some standard DDEs in the reviewed literature. Keywords— Block Method, Collocation Technique, Delay Term, Delay Differential Equation, Self Starting.   

scholarly journals Oscillatory results for second-order noncanonical delay differential equations

2019 ◽  
Vol 39 (4) ◽  
pp. 483-495 ◽  
Author(s):  
Jozef Džurina ◽  
Irena Jadlovská ◽  
Ioannis P. Stavroulakis
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Positive Solutions ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Second Order ◽  
Linear Delay ◽  
Delay Differential

The main purpose of this paper is to improve recent oscillation results for the second-order half-linear delay differential equation \[\left(r(t)\left(y'(t)\right)^\gamma\right)'+q(t)y^\gamma(\tau(t))= 0, \quad t\geq t_0,\] under the condition \[\int_{t_0}^{\infty}\frac{\text{d} t}{r^{1/\gamma}(t)} \lt \infty.\] Our approach is essentially based on establishing sharper estimates for positive solutions of the studied equation than those used in known works. Two examples illustrating the results are given.

An Oscillation Criterion for First Order Linear Delay Differential Equations

1998 ◽  
Vol 41 (2) ◽  
pp. 207-213 ◽  
Author(s):  
CH. G. Philos ◽  
Y. G. Sficas
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Oscillation Criterion ◽  
Order Linear ◽  
First Order ◽  
Linear Delay ◽  
Delay Differential

AbstractA new oscillation criterion is given for the delay differential equation , where and the function T defined by is increasing and such that . This criterion concerns the case where .

scholarly journals Asymptotic properties of trinomial delay differential equations

2009 ◽  
Vol 43 (1) ◽  
pp. 71-79
Author(s):  
Jozef Džurina ◽  
Renáta Kotorová
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Canonical Form ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Asymptotic Properties ◽  
Third Order ◽  
The Third ◽  
Delay Differential ◽  
New Criteria

AbstractNew criteria for asymptotic properties of the solutions of the third order delay differential equation, by transforming this equation to its binomial canonical form are presented

Sign in / Sign up

Export Citation Format

Share Document