Oscillation of second order half-linear neutral differential equations with weaker restrictions on shifted arguments

2020 ◽  
Vol 70 (2) ◽  
pp. 389-400
Author(s):  
Simona Fišnarová ◽  
Robert Mařík
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
New Approach ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Oscillatory Properties

Abstract Neutral differential equations are one of the most important extensions of classical ordinary differential equations and aim to give a better explanation for modeling phenomena where ordinary differential equations are insufficient. Naturally, all the questions studied in the scope of ordinary differential equations attracted the attention also for neutral differential equations. In this paper we study the oscillatory properties of second order half-linear neutral differential equations. We present oscillation criteria derived using a new approach. This approach allows us to reduce common restrictions on the deviations in arguments which are present in the currently known results of this type.

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 differential equations with damping

1990 ◽  
Vol 49 (1) ◽  
pp. 43-54 ◽  
Author(s):  
S. R. Grace
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Nonlinear Ordinary Differential Equations ◽  
Oscillation Criteria ◽  
Second Order Differential Equations ◽  
Linear Differential

AbstractNew oscillation criteria are given for second order nonlinear ordinary differential equations with alternating coefficients. The results involve a condition obtained by Kamenev for linear differential equations. The obtained criterion for superlinear differential equations is a complement of the work established by Kwong and Wong, and Philos, for sublinear differential equations and by Yan for linear differential equations.

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 Integral averaging techniques for the oscillation of second order sublinear ordinarry differential equations

1986 ◽  
Vol 40 (1) ◽  
pp. 111-130 ◽  
Author(s):  
Ch. G. Philos
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Special Cases ◽  
Averaging Techniques

AbstractNew oscillation criteria are established for second order sublinear ordinary differential equations with alternating coefficients. These criteria are obtained by using an integral averaging technique and can be applied in some special cases in which other classical oscillation results are no applicable.

scholarly journals Some New Oscillation Results for Fourth-Order Neutral Differential Equations with Delay Argument

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1248 ◽  
Author(s):  
Omar Bazighifan ◽  
Osama Moaaz ◽  
Rami Ahmad El-Nabulsi ◽  
Ali Muhib
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Delay Argument ◽  
The Right ◽  
Equations With Delay ◽  
Oscillatory Properties

The aim of this paper is to study the oscillatory properties of 4th-order neutral differential equations. We obtain some oscillation criteria for the equation by the theory of comparison. The obtained results improve well-known oscillation results in the literate. Symmetry plays an important role in determining the right way to study these equation. An example to illustrate the results is given.

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.

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