The authors investigate oscillatory properties of the nonlinear second-order differential equation
under natural restrictions on the functions and . Using a modified -function averaging technique introduced for linear equations by Ch. G. Philos [Arch. Math. 53, 482-492 (1989; Zbl 0661.34030)], additional conditions are found which guarantee that (*) possesses no nonoscillatory solution. The results of the paper are illustrated by a number of examples showing that the obtained criteria apply in situations where known criteria fail.