New interval oscillation criteria for second-order functional differential equations with nonlinear damping

Abstract

This paper concerns the oscillation problem of second-order nonlinear damped ODE with functional terms. We give some new interval oscillation criteria which is not only based on constructing a lower solution of a Riccati type equation but also based on constructing an upper solution for corresponding Riccati type equation. We use a recently developed pointwise comparison principle between those lower and upper solutions to obtain our results. Some illustrative examples are also provided to demonstrate our results.