The author investigates oscillation properties of solutions of the nonlinear differential equation
where is a quotient of odd integers, and the nonlinearity satisfies the usual sign condition and for . A typical result is the following statement.
Theorem. Suppose that and
(i) for any ;
(ii) exists and .
Then every solution of (*) is oscillatory.
Proofs of the results presented are essentially based on the generalized Riccati technique consisting in the fact that the quotient satisfies certain Riccati-type differential equation.
The results of the paper extend, among others, oscillation criteria of P. J. Y. Wong and R. P. Agarwal [J. Math. Anal. Appl. 198, No. 2, 337-354 (1996; Zbl 0855.34039)] and in the linear case , oscillation criteria of H. J. Li [J. Math. Anal. Appl. 194, No. 1, 217-234 (1995; Zbl 0836.34033)].