On a Method for Studying the Asymptotics of Solutions of Odd-Order Differential Equations with Oscillating Coefficients

2021 ◽  
Vol 109 (5-6) ◽  
pp. 980-985
Author(s):  
N. F. Valeev ◽  
É. A. Nazirova ◽  
Ya. T. Sultanaev
Keyword(s):  
Differential Equations ◽  
Asymptotics Of Solutions ◽  
Odd Order ◽  
Oscillating Coefficients

scholarly journals New Results for Oscillation of Solutions of Odd-Order Neutral Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1095
Author(s):  
Clemente Cesarano ◽  
Osama Moaaz ◽  
Belgees Qaraad ◽  
Nawal A. Alshehri ◽  
Sayed K. Elagan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Odd Order ◽  
Future Prediction ◽  
Functional Differential ◽  
Delay Differential

Differential equations with delay arguments are one of the branches of functional differential equations which take into account the system’s past, allowing for more accurate and efficient future prediction. The symmetry of the equations in terms of positive and negative solutions plays a fundamental and important role in the study of oscillation. In this paper, we study the oscillatory behavior of a class of odd-order neutral delay differential equations. We establish new sufficient conditions for all solutions of such equations to be oscillatory. The obtained results improve, simplify and complement many existing results.

scholarly journals Oscillation and non-oscillation of some neutral differential equations of odd order

1992 ◽  
Vol 15 (3) ◽  
pp. 509-515 ◽  
Author(s):  
B. S. Lalli ◽  
B. G. Zhang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solution ◽  
Neutral Differential Equation ◽  
Neutral Differential Equations ◽  
Neutral Term ◽  
Odd Order ◽  
Existence Criterion ◽  
Oscillation Of Solutions

An existence criterion for nonoscillatory solution for an odd order neutral differential equation is provided. Some sufficient conditions are also given for the oscillation of solutions of somenth order equations with nonlinearity in the neutral term.

AN ASYMPTOTIC STABILITY THEOREM FOR QUASILINEAR DELAY DIFFERENTIAL EQUATIONS WITH OSCILLATING COEFFICIENTS

2013 ◽  
Vol 24 (11) ◽  
pp. 1350092 ◽  
Author(s):  
NGUYEN TIEN DUNG
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Asymptotic Behavior Of Solutions ◽  
Variable Delays ◽  
Nonlinear Anal ◽  
Oscillating Coefficients ◽  
Several Delays

In this paper, we provide new necessary and sufficient conditions of the asymptotic stability for a class of quasilinear differential equations with several delays and oscillating coefficients. Our results are established by means of fixed point theory and improve those obtained in [J. R. Graef, C. Qian and B. Zhang, Asymptotic behavior of solutions of differential equations with variable delays, Proc. London Math. Soc.81 (2000) 72–92; B. Zhang, Fixed points and stability in differential equations with variable delays, Nonlinear Anal.63 (2005) e233–e242].

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