scholarly journals Oscillation Criteria for Second‐Order Neutral Damped Differential Equations with Delay Argument

10.5772/65909 ◽  
2017 ◽  
Author(s):  
Said R. Grace ◽  
Irena Jadlovská
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Oscillation Criteria ◽  
Delay Argument ◽  
Equations With Delay

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 Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Zhonghai Guo ◽  
Xiaoliang Zhou ◽  
Wu-Sheng Wang
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Oscillation Criteria ◽  
Nonnegative Constant ◽  
Interval Oscillation ◽  
Equations With Delay

We study the following second order mixed nonlinear impulsive differential equations with delay(r(t)Φα(x′(t)))′+p0(t)Φα(x(t))+∑i=1npi(t)Φβi(x(t-σ))=e(t),t≥t0,t≠τk,x(τk+)=akx(τk),x'(τk+)=bkx'(τk),k=1,2,…, whereΦ*(u)=|u|*-1u,σis a nonnegative constant,{τk}denotes the impulsive moments sequence, andτk+1-τk>σ. Some sufficient conditions for the interval oscillation criteria of the equations are obtained. The results obtained generalize and improve earlier ones. Two examples are considered to illustrate the main results.

scholarly journals Interval Oscillation Criteria for Super-Half-Linear Impulsive Differential Equations with Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Zhonghai Guo ◽  
Xiaoliang Zhou ◽  
Wu-Sheng Wang
Keyword(s):  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Riccati Transformation ◽  
Oscillation Criteria ◽  
Nonnegative Constant ◽  
Interval Oscillation ◽  
Equations With Delay

We study the following second-order super-half-linear impulsive differential equations with delay[r(t)φγ(x′(t))]′+p(t)φγ(x(t-σ))+q(t)f(x(t-σ))=e(t),t≠τk,x(t+)=akx(t),x′(t+)=bkx′(t),t=τk, wheret≥t0∈ℝ,φ*(u)=|u|*-1u,σis a nonnegative constant,{τk}denotes the impulsive moments sequence withτ1<τ2<⋯<τk<⋯,lim k→∞τk=∞, andτk+1-τk>σ. By some classical inequalities, Riccati transformation, and two classes of functions, we give several interval oscillation criteria which generalize and improve some known results. Moreover, we also give two examples to illustrate the effectiveness and nonemptiness of our results.

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.

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