scholarly journals New oscillation criteria for third-order neutral differential equations with continuously distributed delay

2018 ◽  
Vol 77 ◽  
pp. 64-71 ◽  
Author(s):  
Shaoqin Gao ◽  
Zimeng Chen ◽  
Wenying Shi
Keyword(s):  
Differential Equations ◽  
Distributed Delay ◽  
Third Order ◽  
Oscillation Criteria ◽  
Continuously Distributed Delay ◽  
Neutral Differential Equations

scholarly journals Symmetry and Its Role in Oscillation of Solutions of Third-Order Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1485
Author(s):  
M. Sathish Kumar ◽  
Omar Bazighifan ◽  
Khalifa Al-Shaqsi ◽  
Fongchan Wannalookkhee ◽  
Kamsing Nonlaopon
Keyword(s):  
Differential Equations ◽  
Essential Role ◽  
Third Order ◽  
Average Technique ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Unbounded Solutions ◽  
Riccati Substitution ◽  
Integral Average ◽  
Oscillation Of Solutions

Symmetry plays an essential role in determining the correct methods for the oscillatory properties of solutions to differential equations. This paper examines some new oscillation criteria for unbounded solutions of third-order neutral differential equations of the form (r2(ς)((r1(ς)(z′(ς))β1)′)β2)′ + ∑i=1nqi(ς)xβ3(ϕi(ς))=0. New oscillation results are established by using generalized Riccati substitution, an integral average technique in the case of unbounded neutral coefficients. Examples are given to prove the significance of new theorems.

scholarly journals Oscillation criteria of third-order neutral differential equations with damping and distributed deviating arguments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yakun Wang ◽  
Fanwei Meng ◽  
Juan Gu
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Riccati Transformation ◽  
Third Order ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Integral Averaging Technique ◽  
Distributed Deviating Arguments ◽  
Generalized Riccati Transformation

AbstractOur objective in this paper is to study the oscillatory and asymptotic behavior of the solutions of third-order neutral differential equations with damping and distributed deviating arguments. New oscillation criteria are established, which are based on a refinement generalized Riccati transformation. An important tool for this investigation is the integral averaging technique. Moreover, we provide an example to illustrate the main results.

Oscillation of certain third-order quasilinear neutral differential equations

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Linlin Yang ◽  
Zhiting Xu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Neutral Differential Equation ◽  
Third Order ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
The Third ◽  
Positive Integers ◽  
Type Oscillation

AbstractIn this paper, new oscillation criteria for the third-order quasilinear neutral differential equation $$\left( {a\left( t \right)\left( {z''\left( t \right)} \right)^\gamma } \right)^\prime + q\left( t \right)x^\gamma \left( {\tau \left( t \right)} \right) = 0, t \geqslant t_0 ,$$ are established, where z(t) = x(t) + p(t)x(δ(t)), and γ is a ratio of odd positive integers. Those results extend the oscillation criteria due to Sun [SUN, Y. G.: New Kamenev-type oscillation criteria for second-order nonlinear differential equations with damping, J. Math. Anal. Appl. 291 (2004) 341–351] to the equation, and complement the existing results in literature. Two examples are provided to illustrate the relevance of our main theorems.

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