Second-order oscillation of forced functional differential equations with oscillatory potentials

New oscillation criteria are established for second-order differential equations containing both delay and advanced arguments of the form, (k(t)x′(t))′+p(t)|x(τ(t))|α−1x(τ(t))+q(t)|x(σ(t))|β−1x(σ(t))=e(t),t≥0(k(t)x′(t))′+p(t)|x(τ(t))|α−1x(τ(t))+q(t)|x(σ(t))|β−1x(σ(t))=e(t),t≥0 where α ≥ 1 and β ≥1; k, p, q, e, τ, σ are continuous real-valued functions; k(t) > 0 is nondecreasing; τ and o are nondecreasing, τ(t) ≥ t, σ(t) ≥ t, and limt → ∞ τ(t) = ∞ The potentials p, q, and e are allowed to change sign and the information on the whole half-line is not required as opposed to the usual case in most articles. Among others, as an application of the results we are able to deduce that every solution of x″(t)+m1sintx(t−π12)+m2costx(t+π6)=cos2t,m1,m2≥0 is oscillatory provided that either m1 orm2 is sufficiently large.