MIXED NONLINEAR OSCILLATION OF SECOND ORDER FORCED DYNAMIC EQUATIONS

By using a technique similar to the one introduced by Kong [J. Math. Anal. Appl. 229 (1999) 258–270] and employing an arithmetic-geometric mean inequality, we establish oscillation criteria for second-order forced dynamic equations on time scales containing mixed nonlinearities of the form p(t)x ∆
∆ + q(t)x σ + Xn i=1 qi(t)|x σ | αi−1x σ = e(t), t ≥ t0 where p, q, qi , e : T → R are right-dense continuous with p > 0, σ is the forward jump operator, x σ (t) := x(σ(t)), and the exponents satisfy α1 > · · · > αm > 1 > αm+1 > · · · αn > 0. The results extend many well-known interval oscillation criteria from continuous case to arbitrary time scales.