Oscillation and Asymptotic Behavior for nth-order Nonlinear Neutral Delay Dynamic Equations on Time Scales

2008 ◽  
Vol 109 (3) ◽  
pp. 703-719 ◽  
Author(s):  
Da-Xue Chen
Keyword(s):  
Asymptotic Behavior ◽  
Time Scales ◽  
Dynamic Equations ◽  
Neutral Delay ◽  
Delay Dynamic Equations

scholarly journals Some Oscillation Criteria for Higher-Order Neutral Emden-Fowler Delay Dynamic Equations on Time Scales

2018 ◽  
Vol 228 ◽  
pp. 01003
Author(s):  
Ying Sui ◽  
Yulong Shi ◽  
Yibin Sun ◽  
Shurong Sun
Keyword(s):  
Time Scales ◽  
Dynamic Equation ◽  
Higher Order ◽  
Delay Equation ◽  
Dynamic Equations ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Delay Dynamic Equations

New oscillation criteria are established for higher-order Emdn-Fowler dynamic equation $ q(v)x^{\beta } (\delta (v)) + (r(v)(z^{{\Delta ^{{n - 1}} }} (v))^{\alpha } )^{\Delta } = 0 $ on time scales, $ z(v): = p(v)x(\tau (v)) + x(v) $ Our results extend and supplement those reported in literatures in the sense that we study a more generalized neutral delay equation and do not require $ r^{\Delta } (v) \ge 0 $ and the commutativity of the jump and delay operators.

scholarly journals Oscillation Criteria of Second-Order Mixed Neutral Delay Dynamic Equations on Time Scales

2018 ◽  
Vol 228 ◽  
pp. 01006
Author(s):  
L M Feng ◽  
Y G Zhao ◽  
Y L Shi ◽  
Z L Han
Keyword(s):  
Time Scales ◽  
Dynamic Equation ◽  
Second Order ◽  
Dynamic Equations ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Neutral Dynamic Equation ◽  
Delay Dynamic Equations ◽  
Oscillation Theorems

In this artical, we consider a second-order neutral dynamic equation on a time scales. A number of oscillation theorems are shown that supplement and extend some known results in the eassay.

scholarly journals Oscillation Theorems for Second-Order Half-Linear Neutral Delay Dynamic Equations with Damping on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Quanxin Zhang ◽  
Shouhua Liu
Keyword(s):  
Time Scales ◽  
Second Order ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation ◽  
Delay Dynamic Equations ◽  
Inequality Technique ◽  
Oscillation Theorems

We establish the oscillation criteria of Philos type for second-order half-linear neutral delay dynamic equations with damping on time scales by the generalized Riccati transformation and inequality technique. Our results are new even in the continuous and the discrete cases.

scholarly journals Oscillatory Behavior of Quasilinear Neutral Delay Dynamic Equations on Time Scales

2010 ◽  
Vol 2010 ◽  
pp. 1-25 ◽  
Author(s):  
Zhenlai Han ◽  
Shurong Sun ◽  
Tongxing Li ◽  
Chenghui Zhang
Keyword(s):  
Time Scales ◽  
Oscillatory Behavior ◽  
Dynamic Equations ◽  
Neutral Delay ◽  
Delay Dynamic Equations
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