Journal of the
Korean Mathematical Society JKMS

This paper is concerned with the asymptotic behavior of solutions of the second-order nonlinear perturbed dynamic equation \[ (r(t)x^{\Delta }(t))^{\Delta }+F(t,x^{\sigma }))=G(t,x^{\sigma },\left( x^{\Delta }\right) ^{\sigma }) \] on a time scale ${\Bbb T}$. By using a new technique we establish some sufficient conditions which ensure that every solution oscillates or converges to zero$.$ Our results improve the known oscillation results on the literature for the perturbed dynamic equations on time scales. Some examples illustrating our main results are given.

Keywords: oscillation, perturbed dynamic equations, time scale

MSC numbers: 34K11, 39A10, 39A99, 34A99, 34C10, 39A11