scholarly journals On asymptotic relationships between two higher order dynamic equations on time scales

2017 ◽  
Vol 73 ◽  
pp. 84-90
Author(s):  
Pavel Řehák
Keyword(s):  
Time Scales ◽  
Higher Order ◽  
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.

Oscillation criteria for higher order nonlinear delay dynamic equations on time scales

2016 ◽  
Vol 66 (3) ◽  
Author(s):  
Xin Wu ◽  
Taixiang Sun
Keyword(s):  
Time Scales ◽  
Dynamic Equation ◽  
Time Scale ◽  
Higher Order ◽  
Dynamic Equations ◽  
Oscillation Criteria ◽  
Arbitrary Time ◽  
Delay Dynamic Equation ◽  
Delay Dynamic Equations ◽  
Nonlinear Delay

AbstractIn this paper, we study the oscillation criteria of the following higher order nonlinear delay dynamic equationon an arbitrary time scalewith

scholarly journals Oscillation for Higher Order Dynamic Equations on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Taixiang Sun ◽  
Qiuli He ◽  
Hongjian Xi ◽  
Weiyong Yu
Keyword(s):  
Time Scales ◽  
Dynamic Equation ◽  
Time Scale ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Higher Order ◽  
Dynamic Equations ◽  
Positive Integers

We investigate the oscillation of the following higher order dynamic equation:{an(t)[(an-1(t)(⋯(a1(t)xΔ(t))Δ⋯)Δ)Δ]α}Δ+p(t)xβ(t)=0, on some time scaleT, wheren≥2,ak(t)  (1≤k≤n)andp(t)are positive rd-continuous functions onTandα,βare the quotient of odd positive integers. We give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero.

scholarly journals Oscillation of Higher Order Linear Impulsive Dynamic Equations on Time Scales

2012 ◽  
Vol 03 (06) ◽  
pp. 581-586
Author(s):  
Chaolong Zhang ◽  
Feiqi Deng
Keyword(s):  
Time Scales ◽  
Higher Order ◽  
Dynamic Equations ◽  
Order Linear
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