scholarly journals Existence of periodic solution for first order nonlinear neutral delay equations

2001 ◽  
Vol 14 (2) ◽  
pp. 189-194 ◽  
Author(s):  
Genqiang Wang ◽  
Jurang Yan
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Neutral Delay ◽  
First Order ◽  
Neutral Delay Differential Equation ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper by using the coincidence degree theory, sufficient conditions are given for the existence of periodic solutions of the first order nonlinear neutral delay differential equation.

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.

scholarly journals On the oscillation of first-order neutral delay differential equations with real coefficients

2002 ◽  
Vol 29 (4) ◽  
pp. 245-249 ◽  
Author(s):  
Ibrahim R. Al-Amri
Keyword(s):  
Differential Equation ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Neutral Delay ◽  
First Order ◽  
Neutral Delay Differential Equation ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
T Tau

We prove sufficient conditions for the oscillation of all solutions of a scalar first-order neutral delay differential equationx˙(t)−cx˙(t−τ)+∑i=1npix(t−σi)=0for all0<c<1,τ,σi>0, andpi∈ℝ,i=1,2,…,n.

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.

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.

PERIODIC SOLUTION FOR GENERALIZED HIGH-ORDER DELAY DIFFERENTIAL EQUATIONS

2010 ◽  
Vol 03 (01) ◽  
pp. 31-43
Author(s):  
Zhibo Cheng ◽  
Jingli Ren ◽  
Stefan Siegmund
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Existence Of Periodic Solutions ◽  
Delay Differential ◽  
New Inequalities

In this paper we consider a generalized n-th order delay differential equation, by applying Mawhin's continuation theory and some new inequalities, we obtain sufficient conditions for the existence of periodic solutions. Moreover, an example is given to illustrate the results.

scholarly journals Necessary and Sufficient Conditions of Oscillation in First Order Neutral Delay Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Songbai Guo ◽  
Youjian Shen ◽  
Binbin Shi
Keyword(s):  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Neutral Delay ◽  
First Order ◽  
Neutral Delay Differential Equation ◽  
Neutral Delay Differential Equations ◽  
Constant Coefficients ◽  
Delay Differential ◽  
Necessary And Sufficient

We are concerned with oscillation of the first order neutral delay differential equation[x(t)−px(t−τ)]′+qx(t−σ)=0with constant coefficients, and we obtain some necessary and sufficient conditions of oscillation for all the solutions in respective cases0<p<1andp>1.

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.

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.

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.

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