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.

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 Oscillations of First Order Linear Delay Differential Equations with positive and negative coefficients

2011 ◽  
Vol 8 (3) ◽  
pp. 806-809
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Oscillation Criteria ◽  
Order Linear ◽  
First Order ◽  
Positive And Negative Coefficients ◽  
All Solutions ◽  
Linear Delay ◽  
Delay Differential

Oscillation criteria are obtained for all solutions of the first-order linear delay differential equations with positive and negative coefficients where we established some sufficient conditions so that every solution of (1.1) oscillate. This paper generalized the results in [11]. Some examples are considered to illustrate our main results.

scholarly journals Oscillation Criteria for Linear Neutral Delay Differential Equations of First Order

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Fatima N. Ahmed ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Order Linear ◽  
First Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

Some new sufficient conditions for oscillation of all solutions of the first-order linear neutral delay differential equations are obtained. Our new results improve many well-known results in the literature. Some examples are inserted to illustrate our 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 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 Third Order Half Linear Neutral Differential Equations

2015 ◽  
Vol 12 (3) ◽  
pp. 625-631
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Oscillation Criterion ◽  
Necessary And Sufficient Conditions ◽  
Third Order ◽  
Neutral Differential Equations ◽  
The Third ◽  
All Solutions ◽  
Necessary And Sufficient

In this paper the oscillation criterion was investigated for all solutions of the third-order half linear neutral differential equations. Some necessary and sufficient conditions are established for every solution of (a(t)[(x(t)±p(t)x(?(t) ) )^'' ]^? )^'+q(t) x^? (?(t) )=0, t?t_0, to be oscillatory. Examples are given to illustrate our main results.

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 Comparison theorems for fourth order differential equations

1986 ◽  
Vol 9 (1) ◽  
pp. 105-109
Author(s):  
Garret J. Etgen ◽  
Willie E. Taylor
Keyword(s):  
Continuous Function ◽  
Differential Equations ◽  
Fourth Order ◽  
Linear Equations ◽  
Oscillation Criterion ◽  
Comparison Theorems ◽  
Positive Continuous Function ◽  
Order Linear ◽  
All Solutions

This paper establishes an apparently overlooked relationship between the pair of fourth order linear equationsyiv−p(x)y=0andyiv+p(x)y=0, wherepis a positive, continuous function defined on[0,∞). It is shown that if all solutions of the first equation are nonoscillatory, then all solutions of the second equation must be nonoscillatory as well. An oscillation criterion for these equations is also given.

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 Oscillation of Nonlinear First Order Neutral Differential Equations

2007 ◽  
Vol 4 (3) ◽  
pp. 485-490
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Integral Conditions ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
First Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

In this paper, the author established some new integral conditions for the oscillation of all solutions of nonlinear first order neutral delay differential equations. Examples are inserted to illustrate the results.

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