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 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 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 Improved Oscillation Results for Functional Nonlinear Dynamic Equations of Second Order

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1897
Author(s):  
Taher S. Hassan ◽  
Yuangong Sun ◽  
Amir Abdel Menaem
Keyword(s):  
Dynamic Equation ◽  
Time Scale ◽  
Nonlinear Dynamic ◽  
Recent Literature ◽  
Second Order ◽  
Dynamic Equations ◽  
Oscillation Criteria ◽  
Arbitrary Time ◽  
Nonlinear Dynamic Equations ◽  
Type Oscillation

In this paper, the functional dynamic equation of second order is studied on an arbitrary time scale under milder restrictions without the assumed conditions in the recent literature. The Nehari, Hille, and Ohriska type oscillation criteria of the equation are investigated. The presented results confirm that the study of the equation in this formula is superior to other previous studies. Some examples are addressed to demonstrate the finding.

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.

scholarly journals Oscillation Criteria for Functional Dynamic Equations with Nonlinearities Given by Riemann-Stieltjes Integral

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yuangong Sun ◽  
Taher S. Hassan
Keyword(s):  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Second Order ◽  
Dynamic Equations ◽  
Stieltjes Integral ◽  
Oscillation Criteria ◽  
Nonlinear Dynamic Equation ◽  
Nonlinear Dynamic Equations

We present new oscillation criteria for the second order nonlinear dynamic equation[r(t)ϕγ(xΔ(t))]Δ+q0(t)ϕγ(x(g0(t)))+∫ab‍q(t,s)ϕα(s)(x(g(t,s)))Δζ(s)=0under mild assumptions. Our results generalize and improve some known results for oscillation of second order nonlinear dynamic equations. Several examples are worked out to illustrate the main results.

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