scholarly journals New Oscillatory Behavior of Third-Order Nonlinear Delay Dynamic Equations on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Li Gao ◽  
Quanxin Zhang ◽  
Shouhua Liu
Keyword(s):  
Time Scales ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Third Order ◽  
Generalized Riccati Transformation ◽  
Delay Dynamic Equations ◽  
Inequality Technique ◽  
Nonlinear Delay

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.

Oscillation for Third-Order Nonlinear Delay Dynamic Equations on Time Scales

2013 ◽  
Vol 475-476 ◽  
pp. 1578-1582
Author(s):  
Shou Hua Liu ◽  
Quan Xin Zhang ◽  
Li Gao
Keyword(s):  
Time Scales ◽  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Neutral Delay ◽  
Third Order ◽  
Generalized Riccati Transformation ◽  
Delay Dynamic Equations ◽  
Inequality Technique ◽  
Nonlinear Delay

The oscillation for certain third-order nonlinear neutral delay dynamic equations on time scales is discussed in this article. By using the generalized Riccati transformation and the inequality technique, three new different sufficient conditions which ensure that every solution is oscillatory or converges to zero are established. The results obtained essentially generalize and improve earlier ones.

scholarly journals Oscillation Theorems for Second-Order Half-Linear Neutral Delay Dynamic Equations with Damping on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Quanxin Zhang ◽  
Shouhua Liu
Keyword(s):  
Time Scales ◽  
Second Order ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation ◽  
Delay Dynamic Equations ◽  
Inequality Technique ◽  
Oscillation Theorems

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.

scholarly journals On the Oscillation for Second-Order Half-Linear Neutral Delay Dynamic Equations on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Quanxin Zhang ◽  
Xia Song
Keyword(s):  
Time Scales ◽  
Second Order ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation ◽  
Delay Dynamic Equations ◽  
Inequality Technique

We discuss oscillation criteria for second-order half-linear neutral delay dynamic equations on time scales by using the generalized Riccati transformation and the inequality technique. Under certain conditions, we establish four new oscillation criteria. Our results in this paper are new even for the cases of𝕋=ℝand𝕋=ℤ.

scholarly journals Oscillation Criteria for Third-Order Nonlinear Neutral Dynamic Equations with Mixed Deviating Arguments on Time Scales

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 552
Author(s):  
Zhiyu Zhang ◽  
Ruihua Feng ◽  
Irena Jadlovská ◽  
Qingmin Liu
Keyword(s):  
Asymptotic Behavior ◽  
Time Scales ◽  
Dynamic Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Riccati Transformation ◽  
Third Order ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Inequality Technique ◽  
Neutral Dynamic Equations

Under a couple of canonical and mixed canonical-noncanonical conditions, we investigate the oscillation and asymptotic behavior of solutions to a class of third-order nonlinear neutral dynamic equations with mixed deviating arguments on time scales. By means of the double Riccati transformation and the inequality technique, new oscillation criteria are established, which improve and generalize related results in the literature. Several examples are given to illustrate the main results.

scholarly journals Oscillation Criteria of Third-Order Nonlinear Damped Dynamic Equations on Time Scales

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Yang-Cong Qiu
Keyword(s):  
Time Scales ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Third Order ◽  
Oscillation Criteria ◽  
Function Classes ◽  
Generalized Riccati Transformation

We establish oscillation criteria of third-order nonlinear damped dynamic equations on time scales of the formr1tr2txΔtγΔΔ+ft, xt,xσt, xgt, xΔt=0by employing functions in some function classes and the generalized Riccati transformation. Two examples are given to show the significance of the conclusions.

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