scholarly journals On the Nonoscillation of Second-Order Neutral Delay Differential Equation with Forcing Term

2008 ◽  
Vol 2008 ◽  
pp. 1-9
Author(s):  
Jin-Zhu Zhang ◽  
Zhen Jin ◽  
Tie-Xiong Su ◽  
Jian-Jun Wang ◽  
Zhi-Yu Zhang ◽  
...  
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Sufficient Conditions ◽  
Nonoscillatory Solution ◽  
Contraction Mapping Principle ◽  
Second Order ◽  
Neutral Delay ◽  
Forcing Term ◽  
Neutral Delay Differential Equation ◽  
Delay Differential

This paper is concerned with nonoscillation of second-order neutral delay differential equation with forcing term. By using contraction mapping principle, some sufficient conditions for the existence of nonoscillatory solution are established. The criteria obtained in this paper complement and extend several known results in the literature. Some examples illustrating our main results are given.

scholarly journals Oscillatory and asymptotic behaviour of a nonlinear second order neutral differential equation

2007 ◽  
Vol 57 (2) ◽  
Author(s):  
R. Rath ◽  
N. Misra ◽  
L. Padhy
Keyword(s):  
Differential Equation ◽  
Asymptotic Behaviour ◽  
Delay Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Neutral Delay ◽  
Neutral Delay Differential Equation ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
T Tau

AbstractIn this paper, necessary and sufficient conditions for the oscillation and asymptotic behaviour of solutions of the second order neutral delay differential equation (NDDE) $$\left[ {r(t)(y(t) - p(t)y(t - \tau ))'} \right]^\prime + q(t)G(y(h(t))) = 0$$ are obtained, where q, h ∈ C([0, ∞), ℝ) such that q(t) ≥ 0, r ∈ C (1) ([0, ∞), (0, ∞)), p ∈ C ([0, ∞), ℝ), G ∈ C (ℝ, ℝ) and τ ∈ ℝ+. Since the results of this paper hold when r(t) ≡ 1 and G(u) ≡ u, therefore it extends, generalizes and improves some known results.

scholarly journals Oscillatory Behaviour of a First-Order Neutral Differential Equation in relation to an Old Open Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
K. C. Panda ◽  
R. N. Rath ◽  
S. K. Rath
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
First Order ◽  
Neutral Delay Differential Equation ◽  
Delay Differential ◽  
Oscillation And Nonoscillation

In this paper, we obtain sufficient conditions for oscillation and nonoscillation of the solutions of the neutral delay differential equation yt−∑j=1kpjtyrjt′+qtGygt−utHyht=ft, where pj and rj for each j and q,u,G,H,g,h, and f are all continuous functions and q≥0,u≥0,ht<t,gt<t, and rjt<t for each j. Further, each rjt, gt, and ht⟶∞ as t⟶∞. This paper improves and generalizes some known results.

Sufficient Conditions for the Oscillation of Delay and Neutral Delay Equations

1988 ◽  
Vol 31 (4) ◽  
pp. 459-466 ◽  
Author(s):  
E. A. Grove ◽  
G. Ladas ◽  
J. Schinas
Keyword(s):  
Differential Equation ◽  
Natural Number ◽  
Delay Differential Equation ◽  
Sufficient Conditions ◽  
Delay Equations ◽  
Neutral Delay ◽  
Neutral Delay Differential Equation ◽  
All Solutions ◽  
Delay Differential

AbstractWe established sufficient conditions for the oscillation of all solutions of the delay differential equationand of the neutral delay differential equationwhere p, q, r and a are nonnegative constants and n is an odd natural number.

scholarly journals Stability Properties of a Discretized Neutral Delay Differential Equation

2013 ◽  
Vol 54 (1) ◽  
pp. 83-92 ◽  
Author(s):  
Jana Hrabalová
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Delay Differential Equation ◽  
Stability Region ◽  
Sufficient Conditions ◽  
Neutral Delay ◽  
Neutral Delay Differential Equation ◽  
Asymptotic Stability Region ◽  
Delay Differential ◽  
Necessary And Sufficient

Abstract The paper discusses the asymptotic stability region of a discretization of a linear neutral delay differential equation x′(t) = ax(t - τ) + bx'(t - τ). We present necessary and sufficient conditions specifying this region and describe some of its properties.

Non-oscillatory criteria for a class of second order non-linear forced neutral-delay differential equations

2009 ◽  
Vol 59 (4) ◽  
Author(s):  
R. Rath ◽  
N. Misra ◽  
P. Mishra
Keyword(s):  
Differential Equation ◽  
Delay Differential Equations ◽  
Bounded Solution ◽  
Sufficient Conditions ◽  
Second Order ◽  
Neutral Delay ◽  
Neutral Delay Differential Equation ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
T Tau

AbstractIn this paper, sufficient conditions are obtained, so that the second order neutral delay differential equation $$ (r(t)(y(t) - p(t)y(t - \tau ))')' + q(t)G(y(h(t)) = f(t) $$ has a positive and bounded solution, where q, h, f ∈ C ([0, ∞), ℝ) such that q(t) ≥ 0, but ≢ 0, h(t) ≤ t, h(t) → ∞ as t → ∞, r ∈ C (1) ([0, ∞), (0, ∞)), p ∈ C (2) [0, ∞), ℝ), G ∈ C(ℝ, ℝ) and τ ∈ ℝ+. In our work r(t) ≡ 1 is admissible and neither we assume G is non-decreasing, xG(x) > 0 for x ≠ 0, nor we take G is Lipschitzian. Hence the results of this paper improve many recent results.

scholarly journals Nonoscillatory solutions of neutral delay differential equations

1993 ◽  
Vol 48 (3) ◽  
pp. 475-483 ◽  
Author(s):  
Ming-Po Chen ◽  
J.S. Yu ◽  
Z.C. Wang
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Nonoscillatory Solution ◽  
Neutral Delay ◽  
Nonoscillatory Solutions ◽  
Neutral Delay Differential Equation ◽  
Neutral Delay Differential Equations ◽  
Image Position ◽  
Delay Differential

Consider the following neutral delay differential equationwhere p ∈ R, τ ∈ (0, ∞), δ ∈ R+ = (0, ∞) and Q ∈ (C([t0, ∞), R). We show that ifthen Equation (*)has a nonoscillatory solution when p ≠ –1. We also deal in detail with a conjecture of Chuanxi, Kulenovic and Ladas, and Györi and Ladas.

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.

Sign in / Sign up

Export Citation Format

Share Document