Comparison tests for the asymptotic behaviour of higher-order dynamic equations of neutral type

2015 ◽  
Vol 27 (5) ◽  
Author(s):  
Başak Karpuz
Keyword(s):  
Asymptotic Behaviour ◽  
Neutral Type ◽  
Higher Order ◽  
Dynamic Equations ◽  
Neutral Delay ◽  
First Order ◽  
Delay Dynamic Equations

AbstractIn this paper, we study oscillation and asymptotic behaviour of higher-order neutral delay dynamic equations, and establish comparison with first-order delay dynamic equations. We also present some examples to show applicability and significance of the new results.

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 Oscillatory behaviour of higher-order nonlinear neutral delay dynamic equations on time scales

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2635-2649
Author(s):  
M.M.A. El-Sheikh ◽  
M.H. Abdalla ◽  
A.M. Hassan
Keyword(s):  
Sufficient Conditions ◽  
Higher Order ◽  
Comparison Theorems ◽  
Dynamic Equations ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
Riccati Technique ◽  
Delay Dynamic Equations ◽  
Positive Integers ◽  
Oscillation Of Solutions

In this paper, new sufficient conditions are established for the oscillation of solutions of the higher order dynamic equations [r(t)(z?n-1(t))?]? + q(t) f(x(?(t)))=0, for t ?[t0,?)T, where z(t):= x(t)+ p(t)x(?(t)), n ? 2 is an even integer and ? ? 1 is a quotient of odd positive integers. Under less restrictive assumptions for the neutral coefficient, we employ new comparison theorems and Generalized Riccati technique.

Oscillatory behavior of higher order nonlinear homogeneous neutral delay dynamic equations with positive and negative coefficients

2018 ◽  
Vol 24 (2) ◽  
pp. 139-154
Author(s):  
Saroj Panigrahi ◽  
P. Rami Reddy
Keyword(s):  
Asymptotic Behavior ◽  
Fourth Order ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Oscillatory Behavior ◽  
Dynamic Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Neutral Delay ◽  
Positive And Negative Coefficients ◽  
Delay Dynamic Equations

Abstract In this paper, we derive some sufficient conditions for the oscillatory and asymptotic behavior of solutions of the higher order nonlinear neutral delay dynamic equation with positive and negative coefficients. The results of this paper extend and generalize the results of [S. Panigrahi and P. Rami Reddy, Oscillatory and asymptotic behavior of fourth order non-linear neutral delay dynamic equations, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 20 2013, 143–163] and [S. Panigrahi, J. R. Graef and P. Rami Reddy, Oscillation results for fourth order nonlinear neutral dynamic equations, Commun. Math. Anal. 15 2013, 11–28]. Examples are included to illustrate the validation of the results.

scholarly journals Oscillation criteria for second-order nonlinear delay dynamic equations of neutral type

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Ming Zhang ◽  
Wei Chen ◽  
MMA El-Sheikh ◽  
RA Sallam ◽  
AM Hassan ◽  
...  
Keyword(s):  
Neutral Type ◽  
Second Order ◽  
Dynamic Equations ◽  
Oscillation Criteria ◽  
Delay Dynamic Equations ◽  
Nonlinear Delay

scholarly journals On the Oscillation of Second Order Nonlinear Neutral Delay Dynamic Equations

2007 ◽  
Vol 14 (4) ◽  
pp. 597-606
Author(s):  
Hassan A. Agwo
Keyword(s):  
Dynamic Equation ◽  
Time Scale ◽  
Second Order ◽  
Dynamic Equations ◽  
Sufficient Condition ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Delay Dynamic Equation ◽  
Neutral Delay Dynamic Equation ◽  
Delay Dynamic Equations

Abstract In this paper we obtain some new oscillation criteria for the second order nonlinear neutral delay dynamic equation (𝑥(𝑡) – 𝑝(𝑡)𝑥(𝑡 – τ 1))ΔΔ + 𝑞(𝑡)𝑓(𝑥(𝑡 – τ 2)) = 0, on a time scale 𝕋. Moreover, a new sufficient condition for the oscillation sublinear equation (𝑥(𝑡) – 𝑝(𝑡)𝑥(𝑡 – τ 1))″ + 𝑞(𝑡)𝑓(𝑥(𝑡 – τ 2)) = 0, is presented, which improves other conditions and an example is given to illustrate our result.

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