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 Ž1989, Math. Nachr. 141, 117 127; 1992, J. Math. Anal. Appl. 171, 220 241.and S. R. Grace and B. S. LalliŽ1990, J. Math. Anal. Appl. 149, 277 311., we do not impose any additional condition on the damping term pŽt.. 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.