Oscillation of Second-Order Nonlinear Delay Dynamic Equations with Damping on Time Scales
We use the generalized Riccati transformation and the inequality technique to establish some new oscillation criteria for the second-order nonlinear delay dynamic equation with damping on a time scale T(r(t)g(x(t), xΔ(t)))Δ+p(t)g(x(t), xΔ(t)) + q(t)f(x(τ(t)))=0, where r(t), p(t), and q(t) are posit...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2014/594376 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We use the generalized Riccati transformation and the inequality technique to establish some new oscillation criteria for the second-order nonlinear delay dynamic equation with damping on a time scale T(r(t)g(x(t), xΔ(t)))Δ+p(t)g(x(t), xΔ(t)) + q(t)f(x(τ(t)))=0, where r(t), p(t), and q(t) are positive right dense continuous (rd-continuous) functions on T. Our results improve and extend some results established by Zhang et al., 2011. Also, our results unify the oscillation of the second-order nonlinear delay differential equation with damping and the second-order nonlinear delay difference equation with damping. Finally, we give some examples to illustrate our main results. |
|---|---|
| ISSN: | 1687-9643 1687-9651 |