Abstract
In this paper, we deal with the asymptotics and oscillation of the solutions of higher-order nonlinear dynamic equations with Laplacian and mixed nonlinearities of the form
{r(n-1)(t)phi alpha(n-1) [(r(n-2)(t)(... (r(1)(t)phi(alpha 1) [x(Delta)(t)])(Delta) ...)Delta)Delta]}(Delta)
+Sigma(nu= 0) p(nu) (t)phi gamma(nu) (x(g(nu) (t))) = 0
on an above-unbounded time scale. By using a generalized Riccati transformation and integral averaging technique we study asymptotic behavior and derive some new oscillation criteria for the cases without any restrictions on g(t) and sigma(t) and when n is even and odd. Our results obtained here extend and improve the results of Chen and Qu (J. Appl. Math. Comput. 44(1-2): 357-377, 2014) and Zhang et al. (Appl. Math. Comput. 275: 324-334, 2016).