scholarly journals New Criteria for Sharp Oscillation of Second-OrderNeutral Delay Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2089
Author(s):  
Irena Jadlovská
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
A Priori ◽  
Nonoscillatory Solution ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
A Priori Bound ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
New Criteria

In this paper, new oscillation criteria for second-order half-linear neutral delay differential equations are established, using a recently developed method of iteratively improved monotonicity properties of a nonoscillatory solution. Our approach allows removing several disadvantages which were commonly associated with the method based on a priori bound for the nonoscillatory solution, and deriving new results which are optimal in a nonneutral case. It is shown that the newly obtained results significantly improve a large number of existing ones.

scholarly journals Third-Order Neutral Delay Differential Equations: New Iterative Criteria for Oscillation

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Osama Moaaz ◽  
Emad E. Mahmoud ◽  
Wedad R. Alharbi
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Iterative Technique ◽  
Neutral Delay ◽  
Third Order ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
New Criterion ◽  
New Criteria

This study is aimed at developing new criteria of the iterative nature to test the oscillation of neutral delay differential equations of third order. First, we obtain a new criterion for the nonexistence of the so-called Kneser solutions, using an iterative technique. Further, we use several methods to obtain different criteria, so that a larger area of the models can be covered. The examples provided strongly support the importance of the new results.

scholarly journals Oscillation Criteria of First Order Neutral Delay Differential Equations with Variable Coefficients

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Fatima N. Ahmed ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Variable Coefficients ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
First Order ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

Some new oscillation criteria are given for first order neutral delay differential equations with variable coefficients. Our results generalize and extend some of the well-known results in the literature. Some examples are considered to illustrate the main results.

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 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.

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