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

Interval oscillation criteria are established for second-order forced delay dynamic equations on time scales containing mixed nonlinearities of the form 􀀀 r.t/ .x .t// C p0.t/ .x. 0.t/// C Xn iD1 pi.t/ i .x. i.t/// D e.t/; t 2 Tt0;1/T where T is a time scale, t0 2 T a fixed number; Tt0;1/T is a time scale interval; .u/ D juj 􀀀1u; the functions r; pi; e V Tt0;1/T ! R are right-dense continuous with r > 0 nondecreasing; k V T ! T are nondecreasing right-dense continuous with k.t/ t, limt!1 k.t/ D 1; and the exponents satisfy 1 > > m > > mC1 > n > 0: All results are new even for T D R and T D Z. Analogous results for related advance type equations are also given, as well as extended delay and advance equations. The theory can be 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.