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

2018 ◽  
Vol 2(2018) (1) ◽  
pp. 307-322
Author(s):  
Merve Zingil ◽  
◽  
Fatma Serap Topal ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Yang-Cong Qiu ◽  
Qi-Ru Wang

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.


2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Shao-Yan Zhang ◽  
Qi-Ru Wang

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.


2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Shouhua Liu ◽  
Quanxin Zhang

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.


2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Yang-Cong Qiu ◽  
Qi-Ru Wang

Using functions in some function classes and a generalized Riccati technique, we establish interval oscillation criteria for second-order nonlinear dynamic equations on time scales of the form(p(t)ψ(x(t))xΔ(t))Δ+f(t,x(σ(t)))=0. The obtained interval oscillation criteria can be applied to equations with a forcing term. An example is included to show the significance of the results.


Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1897
Author(s):  
Taher S. Hassan ◽  
Yuangong Sun ◽  
Amir Abdel Menaem

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.


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