OSCILLATION AND ASYMPTOTIC BEHAVIOR OF THIRD ORDER HALF-LINEAR DELAY DIFFERENTIAL EQUATION WITH “MAXIMA”

2017 ◽  
Vol 97 (1) ◽  
pp. 13-28
Author(s):  
R. Arul ◽  
A. Ashok
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Delay Differential Equation ◽  
Third Order ◽  
Linear Delay ◽  
Delay Differential

scholarly journals On the oscillation of third-order quasi-linear delay differential equations

2011 ◽  
Vol 48 (1) ◽  
pp. 117-123 ◽  
Author(s):  
Tongxing Li ◽  
Chenghui Zhang ◽  
Blanka Baculíková ◽  
Jozef Džurina
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Asymptotic Properties ◽  
Third Order ◽  
The Third ◽  
Linear Delay ◽  
Delay Differential

Abstract The aim of this work is to study asymptotic properties of the third-order quasi-linear delay differential equation , (E) where and τ(t) ≤ t. We establish a new condition which guarantees that every solution of (E) is either oscillatory or converges to zero. These results improve some known results in the literature. An example is given to illustrate the main results.

scholarly journals Oscillation Results for Third-Order Semi-Canonical Quasi-Linear Delay Differential Equations

2021 ◽  
Vol 8 (1) ◽  
pp. 228-238
Author(s):  
K. Saranya ◽  
V. Piramanantham ◽  
E. Thandapani
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Main Idea ◽  
Third Order ◽  
The Third ◽  
Linear Delay ◽  
Delay Differential

Abstract The main purpose of this paper is to study the oscillatory properties of solutions of the third-order quasi-linear delay differential equation ℒ y ( t ) + f ( t ) y β ( σ ( t ) ) = 0 {\cal L}y(t) + f(t){y^\beta }(\sigma (t)) = 0 where ℒy(t) = (b(t)(a(t)(y 0(t)) )0)0 is a semi-canonical differential operator. The main idea is to transform the semi-canonical operator into canonical form and then obtain new oscillation results for the studied equation. Examples are provided to illustrate the importance of the main results.

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