Oscillation criteria for second-order neutral equations with distributed deviating argument

2008 ◽  
Vol 206 (1) ◽  
pp. 485-493 ◽  
Author(s):  
Junhua Zhao ◽  
Fanwei Meng
Keyword(s):  
Second Order ◽  
Neutral Equations ◽  
Oscillation Criteria ◽  
Deviating Argument ◽  
Distributed Deviating Argument

scholarly journals Oscillation Criteria for Even Order Neutral Equations with Distributed Deviating Argument

2010 ◽  
Vol 2010 ◽  
pp. 1-14
Author(s):  
Siyu Zhang ◽  
Fanwei Meng
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Neutral Delay ◽  
Neutral Equations ◽  
Oscillation Criteria ◽  
Deviating Argument ◽  
Neutral Delay Differential Equations ◽  
Distributed Deviating Argument ◽  
Even Order ◽  
Delay Differential

We present new oscillation criteria for the even order neutral delay differential equations with distributed deviating argument[r(t)ψ(x(t))Z(n−1)(t)]′+∫abp(t,ξ)f[x(g(t,ξ))]dσ(ξ)=0,  t≥t0, whereZ(t)=x(t)+q(t)x(t−τ). Assumptions in our theorems are less restrictive, whereas the proofs are significantly simpler compared to those by Wang et al. (2005).

Oscillation theorems for certain second-order nonlinear retarded difference equations

2021 ◽  
Vol 71 (4) ◽  
pp. 871-880
Author(s):  
George E. Chatzarakis ◽  
Said R. Grace ◽  
Irena Jadlovská
Keyword(s):  
Difference Equations ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Neutral Equations ◽  
Oscillation Criteria ◽  
First Order ◽  
Oscillation Theorems

Abstract This paper deals with the oscillation of second-order nonlinear retarded difference equations. We present some new oscillation criteria via comparison with first-order equations whose oscillatory behavior are known. The results are generalized to be applicable to different kinds of neutral equations. An example is also given to demonstrate the applicability of the obtained conditions.

scholarly journals Oscillatory behavior of a second order nonlinear advanced differential equation with mixed neutral terms

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hongwei Shi ◽  
Yuzhen Bai
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Oscillation Criteria ◽  
Order Nonlinear Differential Equation

AbstractIn this paper, we present several new oscillation criteria for a second order nonlinear differential equation with mixed neutral terms of the form $$ \bigl(r(t) \bigl(z'(t)\bigr)^{\alpha }\bigr)'+q(t)x^{\beta } \bigl(\sigma (t)\bigr)=0,\quad t\geq t_{0}, $$(r(t)(z′(t))α)′+q(t)xβ(σ(t))=0,t≥t0, where $z(t)=x(t)+p_{1}(t)x(\tau (t))+p_{2}(t)x(\lambda (t))$z(t)=x(t)+p1(t)x(τ(t))+p2(t)x(λ(t)) and α, β are ratios of two positive odd integers. Our results improve and complement some well-known results which were published recently in the literature. Two examples are given to illustrate the efficiency 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 Non-Linear Neutral Differential Equations with Damping: Oscillation of Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 285
Author(s):  
Saad Althobati ◽  
Jehad Alzabut ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Order Equation ◽  
Second Order ◽  
Riccati Technique ◽  
Neutral Equations ◽  
Neutral Differential Equations ◽  
Main Equation ◽  
Non Linear ◽  
Even Order

The oscillation of non-linear neutral equations contributes to many applications, such as torsional oscillations, which have been observed during earthquakes. These oscillations are generally caused by the asymmetry of the structures. The objective of this work is to establish new oscillation criteria for a class of nonlinear even-order differential equations with damping. We employ different approach based on using Riccati technique to reduce the main equation into a second order equation and then comparing with a second order equation whose oscillatory behavior is known. The new conditions complement several results in the literature. Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples.

scholarly journals Oscillation criteria for second-order nonlinear delay dynamic equations of neutral type

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Ming Zhang ◽  
Wei Chen ◽  
MMA El-Sheikh ◽  
RA Sallam ◽  
AM Hassan ◽  
...  
Keyword(s):  
Neutral Type ◽  
Second Order ◽  
Dynamic Equations ◽  
Oscillation Criteria ◽  
Delay Dynamic Equations ◽  
Nonlinear Delay
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