scholarly journals Oscillatory Behavior of a Class of Second-order Nonlinear Dynamic Equations on Time Scales

2011 ◽  
Vol 1 (6) ◽  
pp. 72-79 ◽  
Author(s):  
Da Xue Chen ◽  
Guang Hui Liu
Keyword(s):  
Time Scales ◽  
Nonlinear Dynamic ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Dynamic Equations ◽  
Nonlinear Dynamic Equations

scholarly journals New Oscillatory Behavior of Second-Order Nonlinear Dynamic Equations with Damping on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Shouhua Liu ◽  
Quanxin Zhang
Keyword(s):  
Time Scales ◽  
Nonlinear Dynamic ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Dynamic Equations ◽  
Oscillation Criteria ◽  
Nonlinear Dynamic Equations

We establish four new oscillation criteria of Grace-type for the second-order nonlinear dynamic equations with damping. These criteria extend known criteria for corresponding dynamic equations. Our results are new even in the continuous and the discrete cases.

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 Second-Order Nonlinear Dynamic Equations on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Shao-Yan Zhang ◽  
Qi-Ru Wang
Keyword(s):  
Time Scales ◽  
Nonlinear Dynamic ◽  
Second Order ◽  
Dynamic Equations ◽  
Riccati Technique ◽  
Oscillation Criteria ◽  
Nonlinear Dynamic Equations ◽  
Generalized Riccati Technique ◽  
Averaging Techniques

This paper is concerned with oscillation of second-order nonlinear dynamic equations of the form on time scales. By using a generalized Riccati technique and integral averaging techniques, we establish new oscillation criteria which handle some cases not covered by known criteria.

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