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

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Yang-Cong Qiu ◽  
Akbar Zada ◽  
Haiyong Qin ◽  
Tongxing Li
Keyword(s):  
Time Scales ◽  
Nonlinear Dynamic ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Damping Term ◽  
Third Order ◽  
Oscillation Criteria ◽  
Nonlinear Dynamic Equations ◽  
Neutral Dynamic Equations

We establish several oscillation criteria for a class of third-order nonlinear dynamic equations with a damping term and a nonpositive neutral coefficient by using the Riccati transformation. Two illustrative examples are presented to show the significance of the results obtained.

scholarly journals Oscillatory and Asymptotic Properties on a Class of Third Nonlinear Dynamic Equations with Damping Term on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-17
Author(s):  
Qinghua Feng ◽  
Huizeng Qin
Keyword(s):  
Time Scales ◽  
Nonlinear Dynamic ◽  
Asymptotic Properties ◽  
The Other ◽  
Dynamic Equations ◽  
Damping Term ◽  
Third Order ◽  
Discrete Analysis ◽  
Other Hand ◽  
Nonlinear Dynamic Equations

We establish some new oscillatory and asymptotic criteria for a class of third-order nonlinear dynamic equations with damping term on time scales. The established results on one hand extend some known results in the literature on the other hand unify continuous and discrete analysis. For illustrating the validity of the established results, we also present some applications for them.

scholarly journals Oscillation of Solutions to Third-Order Nonlinear Neutral Dynamic Equations on Time Scales

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 86
Author(s):  
Yang-Cong Qiu ◽  
Kuo-Shou Chiu ◽  
Said R. Grace ◽  
Qingmin Liu ◽  
Irena Jadlovská
Keyword(s):  
Time Scales ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Third Order ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Neutral Dynamic Equations ◽  
Oscillation Of Solutions

In this paper, we are concerned with the oscillation of solutions to a class of third-order nonlinear neutral dynamic equations on time scales. New oscillation criteria are presented by employing the Riccati transformation and integral averaging technique. Two examples are shown to illustrate the conclusions.

On the oscillation of certain third order nonlinear dynamic equations with a nonlinear damping term

2017 ◽  
Vol 67 (2) ◽  
Author(s):  
Said R. Grace ◽  
John R. Graef ◽  
Ercan Tunç
Keyword(s):  
Nonlinear Dynamic ◽  
Nonlinear Damping ◽  
Dynamic Equations ◽  
Damping Term ◽  
Third Order ◽  
Oscillation Criteria ◽  
Nonlinear Dynamic Equations

AbstractNew oscillation criteria for certain third order nonlinear dynamic equations with a nonlinear damping term are established. Examples to illustrate the results are included.

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 for Third Order Neutral Nonlinear Dynamic Equations with Distributed Deviating Arguments on Time Scales

2014 ◽  
Vol 61 (1) ◽  
pp. 141-161 ◽  
Author(s):  
Taher S. Hassan ◽  
Said R. Grace
Keyword(s):  
Time Scales ◽  
Nonlinear Dynamic ◽  
Dynamic Equations ◽  
Third Order ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Distributed Deviating Arguments ◽  
Nonlinear Dynamic Equations

Abstract Some new oscillation criteria for third order neutral nonlinear dynamic equations with distributed deviating arguments on time scales are established. The obtained results extend, improve and correlate many known oscillation results for third order dynamic equations

scholarly journals Kamenev-Type Oscillation Criteria of Second-Order Nonlinear Dynamic Equations on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Yang-Cong Qiu ◽  
Qi-Ru Wang
Keyword(s):  
Time Scales ◽  
Nonlinear Dynamic ◽  
Second Order ◽  
Dynamic Equations ◽  
Riccati Technique ◽  
Oscillation Criteria ◽  
Function Classes ◽  
Nonlinear Dynamic Equations ◽  
Generalized Riccati Technique ◽  
Type Oscillation

Using functions from some function classes and a generalized Riccati technique, we establish Kamenev-type oscillation criteria for second-order nonlinear dynamic equations on time scales of the form(p(t)ψ(x(t))k∘xΔ(t))Δ+f(t,x(σ(t)))=0. Two examples are included to show the significance of the results.

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