OSCILLATION CRITERIA FOR HIGHER ORDER NONLINEAR NEUTRAL DELAY GENERALIZED $\ALPHA-$DIFFERENCE EQUATIONS

2020 ◽  
Vol 9 (9) ◽  
pp. 7611-7628
Author(s):  
P. V. M. Reddy ◽  
M. M. S. Manuel
Keyword(s):  
Difference Equations ◽  
Higher Order ◽  
Neutral Delay ◽  
Oscillation Criteria

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 A Comparison Theorem for Oscillation of the Even-Order Nonlinear Neutral Difference Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Quanxin Zhang
Keyword(s):  
Difference Equation ◽  
Comparison Theorem ◽  
Difference Equations ◽  
Neutral Delay ◽  
Neutral Difference Equation ◽  
Oscillation Criteria ◽  
Even Order ◽  
Delay Difference Equations ◽  
Delay Difference

A comparison theorem on oscillation behavior is firstly established for a class of even-order nonlinear neutral delay difference equations. By using the obtained comparison theorem, two oscillation criteria are derived for the class of even-order nonlinear neutral delay difference equations. Two examples are given to show the effectiveness of the obtained results.

Existence of Positive Solutions for a Class of Higher-Order Neutral Delay Difference Equations

2011 ◽  
Vol 50-51 ◽  
pp. 761-765
Author(s):  
Dong Hua Wang ◽  
Yu Huan Cui ◽  
Pu Yu Hao
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solutions ◽  
Difference Equations ◽  
Higher Order ◽  
Sufficient Condition ◽  
Neutral Delay ◽  
Existence Of Positive Solutions ◽  
Delay Difference Equations ◽  
Delay Difference

In this paper, a class of higher-order neutral delay difference equations is investigated. Some sufficient condition of the asymptotic behavior and existence of positive solutions for the equations are obtained. At last, we give their applications to some more general equations.

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