The authors study the second-order Emden-Fowler equation
where is a positive absolutely continuous function on . Let be the function defined by , and assume that is bounded away from zero at infinity. Under this condition, the main result of the paper says that if the negative part of , , belongs to , then equation (1) has oscillatory solutions (that is, solutions with arbitrary large zeroes). The authors provide an example that shows that this result, being applicable to nonmonotonous functions , strictly extends previous results of M. Jasny [Cas. Pest. Mat. 85, 78-82 (1960; Zbl 0113.07603)], J. Kurzweil [Cas. Pest. Mat. 85, 357-358 (1960; Zbl 0129.06204)], J. W. Heidel and D. B. Hinton [SIAM J. Math. Anal. 3, 344-351 (1972; Zbl 0243.34062)], L. H. Erbe and J. S. Muldowney [Ann. Mat. Pura Appl., IV. Ser. 109, 23-38 (1976; Zbl 0345.34022)], and K. Chiou [Proc. Am. Math. Soc. 35, 120-122 (1972; Zbl 0262.34026)].