Interval oscillation criteria for second-order forced delay dynamic equations with mixed nonlinearities

i=1 pi(t)Φβi (x(τi(t))) = e(t), t ∈ [t0,∞)T where T is a time scale, t0 ∈ T a fixed number; [t0,∞)T is a time scale interval; Φ∗(u) = |u|∗−1u; the functions r, pi, e : [t0,∞)T → R are right-dense continuous with r > 0 nondecreasing; τk : T → T are nondecreasing right-dense continuous with τk(t) ≤ t , limt→∞ τk(t) = ∞; and the exponents satisfy β1 > · · · > βm > α > βm+1 > · · ·βn > 0. All results are new even for T = R and T = Z. Analogous results for related advance type equations are also given, as well as extended delay and advance equations. The theory canbe applied to second-order dynamic equations regardless of the choice of delta or nabla derivatives. Two examples are provided to illustrate one of the theorems. © 2009 Elsevier Ltd. All rights reserved.