Differential equations with non-monotone arguments: iterative Oscillation results

Abstract

In this paper, we present sufficient conditions, involving limsup, in an explicit iterative form which guarantee the oscillation of all solutions of a differential equation with variable non-monotone argument and non-negative coefficients. Corresponding differential equations of both delay and advanced type are studied. Our conditions essentially improve all the known results in the literature. Examples illustrating the significance of the results are also given.