Oscillation for a second-order neutral differential equation with impulses

2009 ◽  
Vol 215 (1) ◽  
pp. 1-15 ◽  
Author(s):  
E.M. Bonotto ◽  
L.P. Gimenes ◽  
M. Federson
Keyword(s):  
Differential Equation ◽  
Second Order ◽  
Neutral Differential Equation

Oscillation of neutral second order half-linear differential equations without commutativity in deviating arguments

2017 ◽  
Vol 67 (3) ◽  
Author(s):  
Simona Fišnarová ◽  
Robert Mařík
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Neutral Differential Equation ◽  
Linear Differential Equations ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Linear Differential

AbstractIn this paper we derive oscillation criteria for the second order half-linear neutral differential equationwhere Φ(

scholarly journals Noncanonical Neutral DDEs of Second-Order: New Sufficient Conditions for Oscillation

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2026
Author(s):  
Awatif A. Hindi ◽  
Osama Moaaz ◽  
Clemente Cesarano ◽  
Wedad R. Alharbi ◽  
Mohamed A. Abdou
Keyword(s):  
Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Neutral Differential Equation ◽  
First Order ◽  
Riccati Substitution

In this paper, new oscillation conditions for the 2nd-order noncanonical neutral differential equation (a0t((ut+a1tug0t)′)β)′+a2tuβg1t=0, where t≥t0, are established. Using Riccati substitution and comparison with an equation of the first-order, we obtain criteria that ensure the oscillation of the studied equation. Furthermore, we complement and improve the previous results in the literature.

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

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Osama Moaaz ◽  
Ali Muhib ◽  
Saud Owyed ◽  
Emad E. Mahmoud ◽  
Aml Abdelnaser
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Neutral Differential Equation ◽  
Neutral Differential Equations ◽  
New Criteria ◽  
Oscillation Of Solutions

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.

scholarly journals On Oscillatory and Asymptotic Behavior of a Second-Order Nonlinear Damped Neutral Differential Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Ercan Tunç ◽  
Said R. Grace
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Second Order ◽  
Neutral Differential Equation ◽  
Neutral Differential Equations

This paper discusses oscillatory and asymptotic properties of solutions of a class of second-order nonlinear damped neutral differential equations. Some new sufficient conditions for any solution of the equation to be oscillatory or to converge to zero are given. The results obtained extend and improve some of the related results reported in the literature. The results are illustrated with examples.

scholarly journals Homoclinic orbits for a singular second-order neutral differential equation

2010 ◽  
Vol 366 (2) ◽  
pp. 550-560 ◽  
Author(s):  
Chengjun Guo ◽  
Donal O'Regan ◽  
Yuantong Xu ◽  
Ravi P. Agarwal
Keyword(s):  
Differential Equation ◽  
Homoclinic Orbits ◽  
Second Order ◽  
Neutral Differential Equation

Oscillation results for second-order mixed neutral differential equations with distributed deviating arguments

2016 ◽  
Vol 66 (3) ◽  
Author(s):  
Chenghui Zhang ◽  
Blanka Baculíková ◽  
Jozef Džurina ◽  
Tongxing Li
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Neutral Differential Equation ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Distributed Deviating Arguments ◽  
All Solutions

AbstractWe obtain some oscillation criteria for all solutions to a second-order mixed neutral differential equation with distributed deviating arguments. The results presented improve those reported in the literature.

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