scholarly journals Oscillatory Behavior of Euler Type Delay Dynamic Equations withp-Laplacian Like Operators

2018 ◽  
Vol 228 ◽  
pp. 01004
Author(s):  
Ying Sui ◽  
Yulong Shi ◽  
Yige Zhao ◽  
Zhenlai Han

We consider the Euler type delay dynamic equation withp-Laplacin like operators $ (x^{{^{\Delta } }} (v)|x^{{^{\Delta } }} (v)|^{{p - 2}} )^{{^{\Delta } }} + a(v)x^{{^{\Delta } }} (v)|^{{p - 2}} + r(v)x(\delta (v))|x(\delta (v))|^{{p - 2}} = 0 $ , where $ v \in [v_{0} ,\infty ) $ By using new inequality technique, we give some new criteria, which complement related contributions results.

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Li Gao ◽  
Quanxin Zhang ◽  
Shouhua Liu

A class of third-order nonlinear delay dynamic equations on time scales is studied. By using the generalized Riccati transformation and the inequality technique, four new sufficient conditions which ensure that every solution is oscillatory or converges to zero are established. The results obtained essentially improve earlier ones. Some examples are considered to illustrate the main results.


2007 ◽  
Vol 14 (4) ◽  
pp. 597-606
Author(s):  
Hassan A. Agwo

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.


2016 ◽  
Vol 66 (3) ◽  
Author(s):  
Xin Wu ◽  
Taixiang Sun

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


2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Mehmet Ünal ◽  
Youssef N. Raffoul

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.


2018 ◽  
Vol 228 ◽  
pp. 01003
Author(s):  
Ying Sui ◽  
Yulong Shi ◽  
Yibin Sun ◽  
Shurong Sun

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.


2018 ◽  
Vol 228 ◽  
pp. 01006
Author(s):  
L M Feng ◽  
Y G Zhao ◽  
Y L Shi ◽  
Z L Han

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.


2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Quanxin Zhang ◽  
Shouhua Liu

We establish the oscillation criteria of Philos type for second-order half-linear neutral delay dynamic equations with damping on time scales by the generalized Riccati transformation and inequality technique. Our results are new even in the continuous and the discrete cases.


2010 ◽  
Vol 2010 ◽  
pp. 1-25 ◽  
Author(s):  
Zhenlai Han ◽  
Shurong Sun ◽  
Tongxing Li ◽  
Chenghui Zhang

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
I. Kubiaczyk ◽  
S. Saker ◽  
A. Sikorska-Nowak

AbstractIn this paper, we establish some new sufficient conditions for oscillation of the second-order neutral functional dynamic equation $$\left[ {r\left( t \right)\left[ {m\left( t \right)y\left( t \right) + p\left( t \right)y\left( {\tau \left( t \right)} \right)} \right]^\Delta } \right]^\Delta + q\left( t \right)f\left( {y\left( {\delta \left( t \right)} \right)} \right) = 0$$ on a time scale $$\mathbb{T}$$ which is unbounded above, where m, p, q, r, T and δ are real valued rd-continuous positive functions defined on $$\mathbb{T}$$. The main investigation of the results depends on the Riccati substitutions and the analysis of the associated Riccati dynamic inequality. The results complement the oscillation results for neutral delay dynamic equations and improve some oscillation results for neutral delay differential and difference equations. Some examples illustrating our main results are given.


2010 ◽  
Vol 2010 (1) ◽  
pp. 450264 ◽  
Author(s):  
Zhenlai Han ◽  
Shurong Sun ◽  
Tongxing Li ◽  
Chenghui Zhang

Sign in / Sign up

Export Citation Format

Share Document