scholarly journals Even-order differential equation with continuous delay: nonexistence criteria of Kneser solutions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ali Muhib ◽  
M. Motawi Khashan ◽  
Osama Moaaz
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Delay Argument ◽  
Even Order ◽  
Continuous Delay ◽  
New Criteria

AbstractIn this paper, we study even-order DEs where we deduce new conditions for nonexistence Kneser solutions for this type of DEs. Based on the nonexistence criteria of Kneser solutions, we establish the criteria for oscillation that take into account the effect of the delay argument, where to our knowledge all the previous results neglected the effect of the delay argument, so our results improve the previous results. The effectiveness of our new criteria is illustrated by examples.

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 Some Oscillation Results for Even-Order Differential Equations with Neutral Term

2021 ◽  
Vol 5 (4) ◽  
pp. 246
Author(s):  
Maryam Al-Kandari ◽  
Omar Bazighifan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Oscillation Criteria ◽  
Neutral Term ◽  
Even Order ◽  
Riccati Substitution ◽  
Comparison Technique

The objective of this work is to study some new oscillation criteria for even-order differential equation with neutral term rxzn−1xγ′+qxyγζx=0. By using the Riccati substitution and comparison technique, several new oscillation criteria are obtained for the studied equation. Our results generalize and improve some known results in the literature. We offer some examples to illustrate the feasibility of our conditions.

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.

New Asymptotic Stability and Uniqueness Results on Periodic Solutions of Second Order Differential Equations Using Degree Theory

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Manuel Zamora
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Periodic Solutions ◽  
Order Differential Equation ◽  
Degree Theory ◽  
Second Order ◽  
Topological Degree Theory ◽  
Second Order Differential Equations ◽  
Uniqueness Results ◽  
New Criteria

AbstractWe present new criteria for uniqueness and asymptotic stability of periodic solutions of a second order differential equation based on topological degree theory. As an application, we will study some well known equations and some illustrative examples.

scholarly journals Differential equations of even-order with p-Laplacian like operators: qualitative properties of the solutions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Omar Bazighifan ◽  
Thabet Abdeljawad ◽  
Qasem M. Al-Mdallal
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Qualitative Properties ◽  
Middle Term ◽  
Oscillation Criteria ◽  
Even Order ◽  
Oscillation Of Solutions

AbstractIn this paper, we study the oscillation of solutions for an even-order differential equation with middle term, driven by a p-Laplace differential operator of the form $$ \textstyle\begin{cases} ( r ( x ) \Phi _{p}[z^{ ( \kappa -1 ) } ( x ) ] ) ^{\prime }+a ( x ) \Phi _{p}[f ( z^{ ( \kappa -1 ) } ( x ) ) ]+ \sum_{i=1}^{j}q_{i} ( x ) \Phi _{p}[h ( z ( \delta _{i} ( x ) ) ) ]=0, \\ \quad j\geq 1, r ( x ) >0, r^{\prime } ( x ) +a ( x ) \geq 0, x\geq x_{0}>0. \end{cases}$$ { ( r ( x ) Φ p [ z ( κ − 1 ) ( x ) ] ) ′ + a ( x ) Φ p [ f ( z ( κ − 1 ) ( x ) ) ] + ∑ i = 1 j q i ( x ) Φ p [ h ( z ( δ i ( x ) ) ) ] = 0 , j ≥ 1 , r ( x ) > 0 , r ′ ( x ) + a ( x ) ≥ 0 , x ≥ x 0 > 0 . The oscillation criteria for these equations have been obtained. Furthermore, an example is given to illustrate the criteria.

scholarly journals ON OSCILLATION OF SOLUTIONS TO QUASI-LINEAR EMDEN – FOWLER TYPE HIGHER-ORDER DIFFERENTIAL EQUATIONS

2017 ◽  
Vol 21 (6) ◽  
pp. 12-22
Author(s):  
I.V. Astashova
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Nonlinear Equations ◽  
Order Differential Equation ◽  
Oscillatory Solutions ◽  
All Solutions ◽  
Even Order ◽  
And Behavior ◽  
Oscillation Of Solutions ◽  
Higher Order Differential Equations

Existence and behavior of oscillatory solutions to nonlinear equations with regular and singular power nonlinearity are investigated. In particular, the existence of oscillatory solutions is proved for the equation y(n) + P(x; y; y ′ ; : : : ; y(n−1))|y|k sign y = 0; n 2; k ∈ R; k 1; P ̸= 0; P ∈ C(Rn+1): A criterion is formulated for oscillation of all solutions to the quasilinear even-order differential equation y(n) + nΣ−1 i=0 aj(x) y(i) + p(x) |y|ksigny = 0; p ∈ C(R); aj ∈ C(R); j = 0; : : : ; n − 1; k 1; n = 2m; m ∈ N; which generalizes the well-known Atkinson’s and Kiguradze’s criteria. The existence of quasi-periodic solutions is proved both for regular (k 1) and singular (0 k 1) nonlinear equations y(n) + p0 |y|ksigny = 0; n 2; k ∈ R; k 0; k ̸= 1; p0 ∈ R; with (−1)np0 0: A result on the existence of periodic oscillatory solutions is formulated for this equation with n = 4; k 0; k ̸= 1; p0 0:

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