scholarly journals Oscillation Criteria for First Order Neutral Differential Equations with Positive and Negative Coefficients

2001 ◽  
Vol 253 (1) ◽  
pp. 204-214 ◽  
Author(s):  
Xiaosheng Zhang ◽  
Jurang Yan
Keyword(s):  
Differential Equations ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
First Order ◽  
Positive And Negative Coefficients

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.

scholarly journals A New Approach in the Study of Oscillation Criteria of Even-Order Neutral Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 197 ◽  
Author(s):  
Osama Moaaz ◽  
Jan Awrejcewicz ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Delay Equations ◽  
Oscillation Criterion ◽  
New Approach ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
First Order ◽  
Even Order ◽  
New Criterion

Based on the comparison with first-order delay equations, we establish a new oscillation criterion for a class of even-order neutral differential equations. Our new criterion improves a number of existing ones. An illustrative example is provided.

scholarly journals New Oscillation Results for Second-Order Neutral Differential Equations with Deviating Arguments

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1937
Author(s):  
Yakun Wang ◽  
Fanwei Meng
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Second Order ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
First Order ◽  
Delay Differential ◽  
The Right

In this paper, we focus on the second-order neutral differential equations with deviating arguments which are under the canonical condition. New oscillation criteria are established, which are based on a first-order delay differential equation and generalized Riccati transformations. The idea of symmetry is a useful tool, not only guiding us in the right way to study this function but also simplifies our proof. Our results are generalizations of some previous results and we provide an example to illustrate 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 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.

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