New oscillation criteria are established for the second-order differential equation
where and a.e. on . Integral conditions on the functions are given which guarantee the existence of (disjoint) intervals , , as , such that any nontrivial solution to (*) has at least one zero in , which implies oscillation of (*). These integral conditions use “-function” technique introduced by Ch. G. Philos [Arch. Math. 53, 483-492 (1989; Zbl 0661.34030)] and by H. J. Li [J. Math. Anal. Appl. 194, 217-234 (1995; Zbl 0836.34033)]. Some of them are extensions of Kamenev’s and Philos’ type criteria; see I. V. Kamenev [Mat. Zametki 23, 249-251 (1978; Zbl 0408.34031)]. Examples illustrating the oscillation criteria are given, too.