scholarly journals Oscillation Theorems for Second-Order Nonlinear Neutral Delay Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Tongxing Li ◽  
Yuriy V. Rogovchenko
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Neutral Delay ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
Oscillation Theorems

We analyze the oscillatory behavior of solutions to a class of second-order nonlinear neutral delay differential equations. Our theorems improve a number of related results reported in the literature.

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 New Oscillation Theorems for Second-Order Differential Equations with Canonical and Non-Canonical Operator via Riccati Transformation

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1111
Author(s):  
Shyam Sundar Santra ◽  
Abhay Kumar Sethi ◽  
Osama Moaaz ◽  
Khaled Mohamed Khedher ◽  
Shao-Wen Yao
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Second Order ◽  
Riccati Transformation ◽  
Neutral Delay ◽  
Canonical Operator ◽  
Second Order Differential Equations ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
Oscillation Theorems

In this work, we prove some new oscillation theorems for second-order neutral delay differential equations of the form (a(ξ)((v(ξ)+b(ξ)v(ϑ(ξ)))′))′+c(ξ)G1(v(κ(ξ)))+d(ξ)G2(v(ς(ξ)))=0 under canonical and non-canonical operators, that is, ∫ξ0∞dξa(ξ)=∞ and ∫ξ0∞dξa(ξ)<∞. We use the Riccati transformation to prove our main results. Furthermore, some examples are provided to show the effectiveness and feasibility of the main results.

Oscillations of Second Order Neutral Differential Equations

1993 ◽  
Vol 36 (4) ◽  
pp. 485-496 ◽  
Author(s):  
Shigui Ruan
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Neutral Delay Differential Equation ◽  
Image Position ◽  
Delay Differential

AbstractIn this paper, we consider the oscillatory behavior of the second order neutral delay differential equationwhere t ≥ t0,T and σ are positive constants, a,p, q € C(t0, ∞), R),f ∊ C[R, R]. Some sufficient conditions are established such that the above equation is oscillatory. The obtained oscillation criteria generalize and improve a number of known results about both neutral and delay differential equations.

Oscillations of Neutral Delay Differential Equations

1986 ◽  
Vol 29 (4) ◽  
pp. 438-445 ◽  
Author(s):  
G. Ladas ◽  
Y. G. Sficas
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Neutral Delay Differential Equation ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

AbstractThe oscillatory behavior of the solutions of the neutral delay differential equationwhere p, τ, and a are positive constants and Q ∊ C([t0, ∞), ℝ+), are studied.

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