scholarly journals Asymptotic and Oscillatory Behavior of Solutions of a Class of Higher Order Differential Equation

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1434 ◽  
Author(s):  
Elmetwally M. Elabbasy ◽  
Clemente Cesarano ◽  
Omar Bazighifan ◽  
Osama Moaaz
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Delay Differential Equations ◽  
Order Differential Equation ◽  
Higher Order ◽  
Oscillatory Behavior ◽  
Future Developments ◽  
Correct Direction ◽  
Delay Differential ◽  
The Right

The objective of this paper is to study asymptotic behavior of a class of higher-order delay differential equations with a p-Laplacian like operator. Symmetry ideas are often invisible in these studies, but they help us decide the right way to study them, and show us the correct direction for future developments. New oscillation criteria are obtained by employing a refinement of the generalized Riccati transformations and comparison principles. This new theorem complements and improves a number of results reported in the literature. Some examples are provided to illustrate the main results.

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.

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 Behavior of Non-Oscillatory Solutions of Fourth-Order Neutral Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 477 ◽  
Author(s):  
Osama Moaaz ◽  
Rami Ahmad El-Nabulsi ◽  
Omar Bazighifan
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Fourth Order ◽  
Riccati Transformation ◽  
Oscillatory Solutions ◽  
Neutral Differential Equations ◽  
Future Developments ◽  
Generalized Riccati Transformation ◽  
Correct Direction ◽  
The Right

In this paper, we deal with the asymptotics and oscillation of the solutions of fourth-order neutral differential equations of the form r t z ‴ t α ′ + q t x α g t = 0 , where z t : = x t + p t x δ t . By using a generalized Riccati transformation, we study asymptotic behavior and derive some new oscillation criteria. Our results extend and improve some well-known results which were published recently in the literature. Symmetry ideas are often invisible in these studies, but they help us decide the right way to study them, and to show us the correct direction for future developments. An example is given to illustrate the importance of our results.

Delay-Differential Equation Models for Fisheries

1973 ◽  
Vol 30 (7) ◽  
pp. 939-945 ◽  
Author(s):  
Gilbert G. Walter
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Growth Curves ◽  
Fishing Effort ◽  
Oscillatory Behavior ◽  
The Other ◽  
Differential Equation Models ◽  
New Models ◽  
Delay Differential

Two new "simple" fishery models based on delay-differential equations are introduced and compared to three currently used differential equation models. These new models can account for reproductive lag and allow oscillatory behavior of population biomass, but require only catch and effort data for their application. Equilibrium levels are calculated for both models and examples of various types of growth curves are given. Levels of fishing effort which maximize yield are calculated and found in one case to depend on the previous population and in the other to be constant.

scholarly journals Asymptotic behavior for a class of delay differential equations with a forcing term

2003 ◽  
Vol 34 (4) ◽  
pp. 309-316
Author(s):  
Yuji Liu
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Forcing Term ◽  
Delay Differential ◽  
T Tau

We study the asymptotic behavior of solutions of the following forced delay differential equation $$ x'(t)=-p(t)f(x(t-\tau))+r(t),\quad t\ge 0.  \eqno{(*)}$$ It is show that if $ f$ is increasing and $ |f(x)|\le |x|$ for all $ x\in R$, $ \lim_{t\to +\infty} {r(t)\over p(t)}=0$, $ \int_0^{+\infty} p(s)ds=+\infty$ and $ \limsup_{t\to+\infty} \int_{t-\tau}^t p(s)ds

scholarly journals Asymptotic Properties of Solutions of Fourth-Order Delay Differential Equations

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 628 ◽  
Author(s):  
Clemente Cesarano ◽  
Sandra Pinelas ◽  
Faisal Al-Showaikh ◽  
Omar Bazighifan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Order Differential Equation ◽  
Asymptotic Properties ◽  
Riccati Transformation ◽  
Delay Differential ◽  
Oscillation Of Solutions ◽  
Comparison Technique

In the paper, we study the oscillation of fourth-order delay differential equations, the present authors used a Riccati transformation and the comparison technique for the fourth order delay differential equation, and that was compared with the oscillation of the certain second order differential equation. Our results extend and improve many well-known results for oscillation of solutions to a class of fourth-order delay differential equations. Some examples are also presented to test the strength and applicability of the results obtained.

scholarly journals Qualitative Behavior of Solutions of Second Order Differential Equations

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 777 ◽  
Author(s):  
Clemente Cesarano ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Oscillation Criterion ◽  
Qualitative Behavior ◽  
Second Order Differential Equations ◽  
Future Developments ◽  
Correct Direction ◽  
Riccati Substitution ◽  
Delay Differential ◽  
The Right

In this work, we study the oscillation of second-order delay differential equations, by employing a refinement of the generalized Riccati substitution. We establish a new oscillation criterion. Symmetry ideas are often invisible in these studies, but they help us decide the right way to study them, and to show us the correct direction for future developments. We illustrate the results with some examples.

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