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) vertical bar x(tau(t))vertical bar(alpha-1) x(tau(t)) + q(t) vertical bar x(sigma(t))vertical bar(beta-1) x (sigma(t)) = e (t), t >= 0, where alpha >= 1 and beta >= 1; k, p, q, e, tau, sigma are continuous real-valued functions; k(t) > 0 is nondecreasing; tau and sigma are nondecreasing, tau(t) <= t, sigma(t) >= t, and lim(t ->infinity) tau(t) = infinity. 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) + m(1) sintx (t - pi/12) + m(2) costx (t + pi/6) = cos2t, m(1), m(2) >= 0 is oscillatory provided that either m(1) or m(2) is sufficiently large. (c) 2006 Elsevier Ltd. All rights reserved.