New Criteria on the Oscillatory Behavior of Second Order Nonlinear Differential Equations with Mixed Neutral Terms

Abstract

The authors present some new criteria for the oscillation of second order nonlinear differential equations with mixed nonlinear neutral terms and with mixed deviating arguments. The approach used is to linearize the equation under consideration and then deduce the oscillation from that of the linear form. In so doing the authors obtain new oscillation criteria via a comparison with first order equations whose oscillatory behaviors are known. They illustrate their results with some examples.