scholarly journals Asymptotic Criteria of Neutral Differential Equations with Positive and Negative Coefficients and Impulsive Integral Term

2020 ◽  
pp. 2315-2323
Author(s):  
Hussain Ali Mohamad ◽  
Aqeel Jaddoa
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solutions ◽  
Integral Term ◽  
Neutral Differential Equations ◽  
Positive And Negative Coefficients ◽  
All Solutions ◽  
Impulsive Neutral Differential Equations

In this paper, the asymptotic behavior of all solutions of impulsive neutral differential equations with positive and negative coefficients and with impulsive integral term was investigated. Some sufficient conditions were obtained to ensure that all nonoscillatory solutions converge to zero. Illustrative examples were given for the main results.

scholarly journals Oscillation Criteria for Solutions of Neutral Differential Equations of Impulses Effect with Positive and Negative Coefficients

2020 ◽  
Vol 17 (2) ◽  
pp. 0537
Author(s):  
Aqeel Jaddoa et al.
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Conditions ◽  
Neutral Differential Equations ◽  
First Order ◽  
Positive And Negative Coefficients ◽  
Oscillation Property ◽  
All Solutions ◽  
Impulsive Neutral Differential Equations ◽  
Necessary And Sufficient

In this paper, some necessary and sufficient conditions are obtained to ensure the oscillatory of all solutions of the first order impulsive neutral differential equations. Also, some results in the references have been improved and generalized. New lemmas are established to demonstrate the oscillation property. Special impulsive conditions associated with neutral differential equation are submitted. Some examples are given to illustrate the obtained results.

scholarly journals Property of oscillation of first order impulsive neutral differential equations with positive and negative coefficients

2019 ◽  
Vol 11 (1) ◽  
Author(s):  
Hussain Ali Mohamad ◽  
Aqeel Falih Jaddoa
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Variable Coefficients ◽  
Neutral Differential Equations ◽  
First Order ◽  
Positive And Negative Coefficients ◽  
Variable Delays ◽  
Impulsive Neutral Differential Equations ◽  
Necessary And Sufficient

            In this paper, necessary and sufficient conditions for oscillation are obtained, so that every solution of the linear impulsive neutral differential equation with variable delays and variable coefficients oscillates. Most of authors who study the oscillatory criteria of impulsive neutral differential equations, investigate the case of constant delays and variable coefficients. However the points of impulsive in this paper are more general. An illustrate example is given to demonstrate our claim and explain the results.

Oscillation results for higher order nonlinear neutral differential equations with positive and negative coefficients

2015 ◽  
Vol 21 (2) ◽  
Author(s):  
Saroj Panigrahi ◽  
Rakhee Basu
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Asymptotic Behavior Of Solutions ◽  
Banach Fixed Point Theorem ◽  
Neutral Differential Equations ◽  
Positive And Negative Coefficients

AbstractIn this paper, the authors investigated oscillatory and asymptotic behavior of solutions of a class of nonlinear higher order neutral differential equations with positive and negative coefficients. The results in this paper generalize the results of Tripathy, Panigrahi and Basu [Fasc. Math. 52 (2014), 155–174]. We establish new conditions which guarantees that every solution either oscillatory or converges to zero. Moreover, using the Banach Fixed Point Theorem sufficient conditions are obtained for the existence of bounded positive solutions. Examples are considered to illustrate the main results.

Oscillation in Differential Equations with Positive and Negative Coefficients

1990 ◽  
Vol 33 (4) ◽  
pp. 442-451 ◽  
Author(s):  
G. Ladas ◽  
C. Qian
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Neutral Differential Equations ◽  
Positive And Negative Coefficients ◽  
All Solutions ◽  
Linear Delay ◽  
Image Position ◽  
Delay Differential

AbstractWe obtain sufficient conditions for the oscillation of all solutions of the linear delay differential equation with positive and negative coefficientswhereExtensions to neutral differential equations and some applications to the global asymptotic stability of the trivial solution are also given.

scholarly journals Oscillations of First Order Neutral Differential Equations with Positive and Negative Coefficients

2014 ◽  
Vol 11 (4) ◽  
pp. 1624-1628
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Oscillation Criterion ◽  
Order Linear ◽  
Neutral Differential Equations ◽  
First Order ◽  
Positive And Negative Coefficients ◽  
All Solutions

Oscillation criterion is investigated for all solutions of the first-order linear neutral differential equations with positive and negative coefficients. Some sufficient conditions are established so that every solution of eq.(1.1) oscillate. Generalizing of some results in [4] and [5] are given. Examples are given to illustrated our main results.

On oscillatory fourth order nonlinear neutral differential equations – III

2018 ◽  
Vol 68 (6) ◽  
pp. 1385-1396 ◽  
Author(s):  
Arun Kumar Tripathy ◽  
Rashmi Rekha Mohanta
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Neutral Differential Equations ◽  
All Solutions ◽  
Functional Differential ◽  
T Tau

Abstract In this paper, several sufficient conditions for oscillation of all solutions of fourth order functional differential equations of neutral type of the form $$\begin{array}{} \displaystyle \bigl(r(t)(y(t)+p(t)y(t-\tau))''\bigr)''+q(t)G\bigl(y(t-\sigma)\bigr)=0 \end{array}$$ are studied under the assumption $$\begin{array}{} \displaystyle \int\limits^{\infty}_{0}\frac{t}{r(t)}{\rm d} t =\infty \end{array}$$

scholarly journals On the oscillation of a nonlinear two-dimensional difference systems

2001 ◽  
Vol 32 (3) ◽  
pp. 201-209 ◽  
Author(s):  
E. Thandapani ◽  
B. Ponnammal
Keyword(s):  
Asymptotic Behavior ◽  
Sufficient Conditions ◽  
Real Sequence ◽  
Two Dimensional ◽  
Difference System ◽  
Nonoscillatory Solutions ◽  
Difference Systems ◽  
All Solutions ◽  
Necessary And Sufficient ◽  
Strongly Sublinear

The authors consider the two-dimensional difference system$$ \Delta x_n = b_n g (y_n) $$ $$ \Delta y_n = -f(n, x_{n+1}) $$where $ n \in N(n_0) = \{ n_0, n_0+1, \ldots \} $, $ n_0 $ a nonnegative integer; $ \{ b_n \} $ is a real sequence, $ f: N(n_0) \times {\rm R} \to {\rm R} $ is continuous with $ u f(n,u) > 0 $ for all $ u \ne 0 $. Necessary and sufficient conditions for the existence of nonoscillatory solutions with a specified asymptotic behavior are given. Also sufficient conditions for all solutions to be oscillatory are obtained if $ f $ is either strongly sublinear or strongly superlinear. Examples of their results are also inserted.

scholarly journals First Order Nonlinear Neutral Delay Differential Equations

2004 ◽  
Vol 1 (2) ◽  
pp. 347-349 ◽  
Author(s):  
Baghdad Science Journal
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Neutral Delay ◽  
Nonoscillatory Solutions ◽  
Neutral Differential Equations ◽  
First Order ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

The author obtain results on the asymptotic behavior of the nonoscillatory solutions of first order nonlinear neutral differential equations. Keywords. Neutral differential equations, Oscillatory and Nonoscillatory solutions.

Asymptotic Behavior for Nonoscillatory Solutions of Second Order Nonlinear Functional Differential Equation

2012 ◽  
Vol 616-618 ◽  
pp. 2137-2141
Author(s):  
Zhi Min Luo ◽  
Bei Fei Chen
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solutions ◽  
Nonlinear Functional ◽  
Nonlinear Functional Differential Equation ◽  
Functional Differential

This paper studied the asymptotic behavior of a class of nonlinear functional differential equations by using the Bellman-Bihari inequality. We obtain results which extend and complement those in references. The results indicate that all non-oscillatory continuable solutions of equation are asymptotic to at+b as under some sufficient conditions, where a,b are real constants. An example is provided to illustrate the application of the results.

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