Oscillation of Emden–Fowler type nonlinear neutral delay dynamic equation on time scales

2018 ◽  
Vol 60 (1-2) ◽  
pp. 291-301
Author(s):  
Ying Sui ◽  
Shurong Sun
Keyword(s):  
Time Scales ◽  
Dynamic Equation ◽  
Neutral Delay ◽  
Delay Dynamic Equation ◽  
Neutral Delay Dynamic Equation

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 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.

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 behavior of third-order quasilinear neutral delay dynamic equations on time scales

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1425-1436 ◽  
Author(s):  
Nadide Utku ◽  
Mehmet Şenel
Keyword(s):  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Neutral Delay ◽  
Third Order ◽  
The Third ◽  
Delay Dynamic Equation ◽  
Integral Averaging Technique ◽  
Neutral Delay Dynamic Equation ◽  
Generalized Riccati Transformation ◽  
Delay Dynamic Equations

The aim of this paper is to give oscillation criteria for the third-order quasilinear neutral delay dynamic equation [r(t)([x(t)+ p(t)x(?0(t))]??)?]? + q1(t)x?(?1(t)) + q2(t)x?(?2(t)) = 0; on a time scale T, where 0 < ? < ? < ?. By using a generalized Riccati transformation and integral averaging technique, we establish some new sufficient conditions which ensure that every solution of this equation oscillates or converges to zero.

scholarly journals Qualitative Analysis of Solutions of Nonlinear Delay Dynamic Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Mehmet Ünal ◽  
Youssef N. Raffoul
Keyword(s):  
Fixed Point ◽  
Qualitative Analysis ◽  
Time Scales ◽  
Dynamic Equation ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Dynamic Equations ◽  
Delay Dynamic Equation ◽  
Delay Dynamic Equations ◽  
Nonlinear Delay

We use the fixed point theory to investigate the qualitative analysis of a nonlinear delay dynamic equation on an arbitrary time scales. We illustrate our results by applying them to various kind of time scales.

An asymptotic result for a certain type of delay dynamic equation with biological background

2020 ◽  
Vol 43 (12) ◽  
pp. 7303-7310
Author(s):  
Halis Can Koyuncuoğlu ◽  
Nezihe Turhan ◽  
Murat Adıvar
Keyword(s):  
Dynamic Equation ◽  
Asymptotic Result ◽  
Delay Dynamic Equation
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