Oscillation results for a second order damped differential equation with nonmonotonous nonlinearity

We present new oscillation criteria for a nonlinear second order differential equation with a damping term. An essential feature of our results is that we do not require the nonlinearity to be nondecreasing. Furthermore, as opposed to the recent results by S. R. Grace (1989, Math. Nachr. 141, 117-127; 1992 J. Math. Anal. Appl. 171, 220-241) and S. R. Grace and B. S. Lalli (1990, J. Math. Anal. Appl. 149, 277-311), we do not impose any additional condition on the damping term p(t). Consequently, our theorems apply to new classes of equations which are not covered by the known criteria. The relevance of the results obtained is illustrated with a number of carefully selected examples. (C) 2000 Academic Press.