New stability theorem for uncertain pantograph differential equations

2021 ◽  
Vol 40 (5) ◽  
pp. 9403-9411
Author(s):  
Zhifu Jia ◽  
Xinsheng Liu ◽  
Yu Zhang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Stability Theorem ◽  
Sufficient Condition ◽  
Stability In Distribution ◽  
Delay Differential

Uncertain pantograph differential equation (UPDE for short) is a special unbounded uncertain delay differential equation. Stability in measure, stability almost surely and stability in p-th moment for uncertain pantograph differential equation have been investigated, which are not applicable for all situations, for the sake of completeness, this paper mainly gives the concept of stability in distribution, and proves the sufficient condition for uncertain pantograph differential equation being stable in distribution. In addition, the relationships among stability almost surely, stability in measure, stability in p-th moment, and stability in distribution for the uncertain pantograph differential equation are also discussed.

scholarly journals Iterative criteria for bounds on the growth of positive solutions of a delay differential equation

1978 ◽  
Vol 25 (2) ◽  
pp. 195-200
Author(s):  
Raymond D. Terry
Keyword(s):  
Differential Equation ◽  
Positive Solutions ◽  
Delay Differential Equation ◽  
Sufficient Condition ◽  
All Solutions ◽  
Image Position ◽  
Delay Differential

AbstractFollowing Terry (Pacific J. Math. 52 (1974), 269–282), the positive solutions of eauqtion (E): are classified according to types Bj. We denote A neccessary condition is given for a Bk-solution y(t) of (E) to satisfy y2k(t) ≥ m(t) > 0. In the case m(t) = C > 0, we obtain a sufficient condition for all solutions of (E) to be oscillatory.

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 New Oscillation and Nonoscillation Criteria for a Class of Linear Delay Differential Equation

2019 ◽  
Vol 8 (10) ◽  
pp. 308-313
Keyword(s):  
Differential Equation ◽  
Continuous Function ◽  
Delay Differential Equation ◽  
Sufficient Condition ◽  
First Order ◽  
Linear Delay ◽  
Piecewise Continuous ◽  
Delay Differential ◽  
Oscillation And Nonoscillation Criteria ◽  
Oscillation And Nonoscillation

In this article the authors established sufficient condition for the first order delay differential equation in the form , ( ) where , = and is a non negative piecewise continuous function. Some interesting examples are provided to illustrate the results. Keywords: Oscillation, delay differential equation and bounded. AMS Subject Classification 2010: 39A10 and 39A12.

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 Oscillation of Nonlinear Differential Equations with Advanced Arguments

2008 ◽  
Vol 5 (4) ◽  
pp. 652-659
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solution ◽  
Oscillatory Solutions ◽  
All Solutions ◽  
Delay Differential ◽  
Necessary And Sufficient

This paper is concerned with the oscillation of all solutions of the n-th order delay differential equation . The necessary and sufficient conditions for oscillatory solutions are obtained and other conditions for nonoscillatory solution to converge to zero are established.

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

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