scholarly journals Oscillation Criteria for Fourth-Order Nonlinear Dynamic Equations on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Xin Wu ◽  
Taixiang Sun ◽  
Hongjian Xi ◽  
Changhong Chen
Keyword(s):  
Time Scales ◽  
Fourth Order ◽  
Nonlinear Dynamic ◽  
Dynamic Equations ◽  
Oscillation Criteria ◽  
Nonlinear 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.

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.

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.

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