On forced oscillation of higher order functional differential equations

摘要

In this paper, we establish some new oscillation criteria for the following forced functional differential equationx(n)(t)+q(t)|x(τ(t))|λ-1x(τ(t))=e(t),t∈[t0,∞).No restriction is imposed on the forcing term e(t) to be the nth derivative of an oscillatory function. Two cases have been taken into consideration: (i) q(t)<0,λ>1 and τ(t)⩽t(⩾t); (ii) q(t) changes its sign, 0 < λ < 1 and τ(t)⩽t(⩾t). The main results generalize some existing results and can be applied to the oscillation problem that are not covered in the literature.