scholarly journals Amended oscillation criteria for second-order neutral differential equations with damping term

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Osama Moaaz ◽  
George E. Chatzarakis ◽  
Thabet Abdeljawad ◽  
Clemente Cesarano ◽  
Amany Nabih
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Application Area ◽  
Damping Term ◽  
Oscillation Criteria ◽  
Neutral Differential Equations

Abstract The aim of this work is to improve the oscillation results for second-order neutral differential equations with damping term. We consider the noncanonical case which always leads to two independent conditions for oscillation. We are working to improve related results by simplifying the conditions, based on taking a different approach that leads to one condition. Moreover, we obtain different forms of conditions to expand the application area. An example is also given to demonstrate the applicability and strength of the obtained conditions over known ones.

scholarly journals Oscillation Criteria for Second Order Neutral Differential Equations

1996 ◽  
Vol 48 (4) ◽  
pp. 871-886 ◽  
Author(s):  
Horng-Jaan Li ◽  
Wei-Ling Liu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Second Order ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Neutral Delay Differential Equation ◽  
Image Position ◽  
Delay Differential

AbstractSome oscillation criteria are given for the second order neutral delay differential equationwhere τ and σ are nonnegative constants, . These results generalize and improve some known results about both neutral and delay differential equations.

scholarly journals Oscillation Criteria for Certain Second-Order Nonlinear Neutral Differential Equations of Mixed Type

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Zhenlai Han ◽  
Tongxing Li ◽  
Chenghui Zhang ◽  
Ying Sun
Keyword(s):  
Differential Equations ◽  
Mixed Type ◽  
Second Order ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Equations Of Mixed Type ◽  
Positive Integers

Some oscillation criteria are established for the second-order nonlinear neutral differential equations of mixed type[(x(t)+p1x(t−τ1)+p2x(t+τ2))γ]′​′=q1(t)xγ(t−σ1)+q2(t)xγ(t+σ2),t≥t0, whereγ≥1is a quotient of odd positive integers. Our results generalize the results given in the literature.

scholarly journals Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Tongxing Li ◽  
Zhenlai Han ◽  
Chenghui Zhang ◽  
Hua Li
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Oscillation Criteria ◽  
Neutral Differential Equations

Some oscillation criteria are established for the second-order superlinear neutral differential equations(r(t)|z'(t)|α-1z'(t))'+f(t,x(σ(t)))=0,t≥t0, wherez(t)=x(t)+p(t)x(τ(t)),τ(t)≥t,σ(t)≥t,p∈C([t0,∞),[0,p0]), andα≥1. Our results are based on the cases∫t0∞1/r1/α(t)dt=∞or∫t0∞1/r1/α(t)dt<∞. Two examples are also provided to illustrate these results.

scholarly journals Improved Oscillation Criteria for 2nd-Order Neutral Differential Equations with Distributed Deviating Arguments

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 849
Author(s):  
Osama Moaaz ◽  
Rami Ahmad El-Nabulsi ◽  
Waad Muhsin ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Comparison Principles ◽  
Neutral Differential Equations ◽  
Distributed Deviating Arguments ◽  
Oscillation Of Solutions

In this study, we establish new sufficient conditions for oscillation of solutions of second-order neutral differential equations with distributed deviating arguments. By employing a refinement of the Riccati transformations and comparison principles, we obtain new oscillation criteria that complement and improve some results reported in the literature. Examples are provided to illustrate the main results.

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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