Global bifurcation results for nonlinear dynamic equations on time scales

2020 ◽  
Vol 269 (12) ◽  
pp. 11252-11278
Author(s):  
Pierluigi Benevieri ◽  
Jaqueline G. Mesquita ◽  
Aldo Pereira
Keyword(s):  
Time Scales ◽  
Nonlinear Dynamic ◽  
Global Bifurcation ◽  
Dynamic Equations ◽  
Nonlinear Dynamic Equations

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 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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