scholarly journals Oscillation Criteria for Second Order Neutral Differential Equations

1996 ◽  
Vol 48 (4) ◽  
pp. 871-886 ◽  
Author(s):  
Horng-Jaan Li ◽  
Wei-Ling Liu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Second Order ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Neutral Delay Differential Equation ◽  
Image Position ◽  
Delay Differential

AbstractSome oscillation criteria are given for the second order neutral delay differential equationwhere τ and σ are nonnegative constants, . These results generalize and improve some known results about both neutral and delay differential equations.

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.

scholarly journals Oscillation results for second order half-linear neutral delay differential equations with "maxima"

2017 ◽  
Vol 48 (3) ◽  
pp. 289-299 ◽  
Author(s):  
Selvarangam Srinivasan ◽  
Rani Bose ◽  
Ethiraju Thandapani
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Second Order ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Neutral Delay Differential Equation ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

In this paper, we present some oscillation criteria for the second order half-linear neutral delay differential equation with ``maxima" of the from\begin{equation*}\left(r(t)((x(t)+p(t)x(\tau(t)))')^{\alpha}\right)'+q(t) \max_{[\sigma(t),\;t]}x^{\alpha}(s)=0\end{equation*}under the condition $\int_{t_0}^{\infty}\frac{1}{r^{1/ \alpha}(t)}dt<\infty.$ The results obtained here extend and complement to some known results in the literature. Examples are provided in support of our results.

scholarly journals On the Asymptotic Behavior of a Class of Second-Order Non-Linear Neutral Differential Equations with Multiple Delays

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 134 ◽  
Author(s):  
Shyam Sundar Santra ◽  
Ioannis Dassios ◽  
Tanusri Ghosh
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Oscillation Theory ◽  
Second Order ◽  
Multiple Delays ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Neutral Delay Differential Equation ◽  
Non Linear ◽  
Delay Differential

In this work, we present some new sufficient conditions for the oscillation of a class of second-order neutral delay differential equation. Our oscillation results, complement, simplify and improve recent results on oscillation theory of this type of non-linear neutral differential equations that appear in the literature. An example is provided to illustrate the value of the main results.

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.

scholarly journals New Oscillation Criteria for Second-Order Neutral Delay Differential Equations with Positive and Negative Coefficients

2010 ◽  
Vol 2010 ◽  
pp. 1-11
Author(s):  
Yuzhen Bai ◽  
Lihua Liu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Second Order ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Positive And Negative Coefficients ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

We establish the oscillation and asymptotic criteria for the second-order neutral delay differential equations with positive and negative coefficients having the forms[x(t)+∑i∈Rci(t)x(αi(t))]′′+r(t)[x(t)+∑i∈Rci(t)x(αi(t))]′+∑i∈Ppi(t)x(βi(t))-∑i∈Qqi(t)x(γi(t))=0and[x(t)+∑i∈Rci(t)x(αi(t))]′′+r(t)[x(t)+∑i∈Rci(t)x(αi(t))]′+∑i∈Ppi(t)x(βi(t))-∑i∈Qqi(t)x(γi(t))=f(t). The obtained new oscillation criteria extend and improve the recent results given in the paperof B. Karpuz et al. (2009).

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