Oscillation of Even Order Damped Neutral Delay Differential Equations with Mixed Nonlinearities

2012 ◽  
Author(s):  
Yi-Bing Sun ◽  
Zhen-Lai Han
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Neutral Delay ◽  
Neutral Delay Differential Equations ◽  
Mixed Nonlinearities ◽  
Even Order ◽  
Delay Differential

scholarly journals Oscillation Criteria for Certain Even Order Neutral Delay Differential Equations with Mixed Nonlinearities

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Zhen-Lai Han ◽  
Yi-Bing Sun ◽  
Yan Zhao ◽  
Dian-Wu Yang
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Neutral Delay Differential Equations ◽  
Mixed Nonlinearities ◽  
Even Order ◽  
Delay Differential

We establish some oscillation criteria for the following certain even order neutral delay differential equations with mixed nonlinearities:rtzn-1tα-1zn-1t'+q0(t)(xτ0tα-1x(τ0(t))+q1t(x(τ1(t))β-1x(τ1(t))+q2t(x(τ2(t))γ-1x(τ2(t))=0, t≥t0,wherez(t)=x(t)+p(t)x(σ(t)),nis even integer, andγ>α>β>0.Our results generalize and improve some known results for oscillation of certain even order neutral delay differential equations with mixed nonlinearities.

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).

scholarly journals Some New Oscillation Criteria of Even-Order Quasi-Linear Delay Differential Equations with Neutral Term

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2074
Author(s):  
Rongrong Guo ◽  
Qingdao Huang ◽  
Qingmin Liu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Neutral Type ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Neutral Term ◽  
Linear Delay ◽  
Neutral Delay Differential Equations ◽  
Even Order ◽  
Delay Differential

The neutral delay differential equations have many applications in the natural sciences, technology, and population dynamics. In this paper, we establish several new oscillation criteria for a kind of even-order quasi-linear neutral delay differential equations. Comparing our results with those in the literature, our criteria solve more general delay differential equations with neutral type, and our results expand the range of neutral term coefficient. Some examples are given to illustrate our conclusions.

scholarly journals New oscillation theorems for a class of even-order neutral delay differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mona Anis ◽  
Osama Moaaz
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Neutral Delay Differential Equations ◽  
Even Order ◽  
Delay Differential ◽  
Oscillation Theorems ◽  
Appl Math

AbstractIn this work, we study the oscillatory behavior of even-order neutral delay differential equations $\upsilon ^{n}(l)+b(l)u(\eta (l))=0$ υ n ( l ) + b ( l ) u ( η ( l ) ) = 0 , where $l\geq l_{0}$ l ≥ l 0 , $n\geq 4$ n ≥ 4 is an even integer and $\upsilon =u+a ( u\circ \mu ) $ υ = u + a ( u ∘ μ ) . By deducing a new iterative relationship between the solution and the corresponding function, new oscillation criteria are established that improve those reported in (T. Li, Yu.V. Rogovchenko in Appl. Math. Lett. 61:35–41, 2016).

scholarly journals Oscillation Criteria for Certain Even Order Neutral Delay Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Ruba Al-Hamouri ◽  
Ali Zein
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Neutral Delay Differential Equations ◽  
Even Order ◽  
Delay Differential ◽  
Oscillation Of Solutions

We establish sufficient conditions for the oscillation of solutions of even order neutral type differential equations of the form[r(t)[x(t)+p(t)x(τ(t))](n−1)]′+q(t)f(x(σ(t)))=0.

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