scholarly journals On oscillatory and asymptotic behavior of fourth order non-linear neutral delay dynamic equations

2011 ◽  
Vol 62 (11) ◽  
pp. 4258-4271 ◽  
Author(s):  
S. Panigrahi ◽  
P. Rami Reddy
Keyword(s):  
Asymptotic Behavior ◽  
Fourth Order ◽  
Dynamic Equations ◽  
Neutral Delay ◽  
Non Linear ◽  
Delay Dynamic Equations

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.

On oscillatory and asymptotic behavior of fourth order nonlinear neutral delay dynamic equations with positive and negative coefficients

2014 ◽  
Vol 64 (2) ◽  
Author(s):  
John Graef ◽  
Saroj Panigrahi ◽  
P. Reddy
Keyword(s):  
Fixed Point ◽  
Fourth Order ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Neutral Delay ◽  
Positive And Negative Coefficients ◽  
Delay Dynamic Equations ◽  
Krasnosel’Skii’S Fixed Point Theorem ◽  
Neutral Dynamic Equations

AbstractIn this paper, oscillatory and asymptotic properties of solutions of nonlinear fourth order neutral dynamic equations of the form $(r(t)(y(t) + p(t)y(\alpha _1 (t)))^{\Delta ^2 } )^{\Delta ^2 } + q(t)G(y(\alpha _2 (t))) - h(t)H(y(\alpha _3 (t))) = 0(H)$ and $(r(t)(y(t) + p(t)y(\alpha _1 (t)))^{\Delta ^2 } )^{\Delta ^2 } + q(t)G(y(\alpha _2 (t))) - h(t)H(y(\alpha _3 (t))) = f(t),(NH)$ are studied on a time scale $\mathbb{T}$ under the assumption that $\int\limits_{t_0 }^\infty {\tfrac{t} {{r(t)}}\Delta t = \infty } $ and for various ranges of p(t). In addition, sufficient conditions are obtained for the existence of bounded positive solutions of the equation (NH) by using Krasnosel’skii’s fixed point theorem.

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 Theorems for Fourth-Order Half-Linear Delay Dynamic Equations with Damping

2013 ◽  
Vol 11 (2) ◽  
pp. 463-475 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Martin Bohner ◽  
Tongxing Li ◽  
Chenghui Zhang
Keyword(s):  
Fourth Order ◽  
Dynamic Equations ◽  
Linear Delay ◽  
Delay Dynamic Equations ◽  
Oscillation Theorems

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.

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.

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